Find the relative maximum, relative minimum, and zeros of each function. y=2 x³-23 x²+78 x-72 .
Answers
the relative maximum occurs at x = (23 - √61) / 6, the relative minimum occurs at x = (23 + √61) / 6.
To find the relative maximum, relative minimum, and zeros of the function y = 2x³ - 23x² + 78x - 72, we need to determine the critical points and analyze the behavior of the function.
First, let's find the derivative of the function:
y' = 6x² - 46x + 78
To find the critical points, we set y' equal to zero and solve for x:
6x² - 46x + 78 = 0
This quadratic equation can be solved using factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values a = 6, b = -46, and c = 78, we get:
x = (-(-46) ± √((-46)² - 4 * 6 * 78)) / (2 * 6)
x = (46 ± √(2116 - 1872)) / 12
x = (46 ± √244) / 12
x = (46 ± 2√61) / 12
x = (23 ± √61) / 6
Now, we have two critical points: (23 + √61) / 6 and (23 - √61) / 6.
To determine the nature of these critical points, we need to analyze the second derivative. Let's find the second derivative of the function:
y'' = 12x - 46
Now, let's evaluate the second derivative at the critical points:
For x = (23 + √61) / 6:
y'' = 12 * (23 + √61) / 6 - 46
y'' = 2√61 - 34
For x = (23 - √61) / 6:
y'' = 12 * (23 - √61) / 6 - 46
y'' = -2√61 - 34
Analyzing the second derivative, we observe the following:
1. If y'' > 0, then the function has a relative minimum at that point.
2. If y'' < 0, then the function has a relative maximum at that point.
3. If y'' = 0, the test is inconclusive.
Let's now analyze the nature of the critical points:
For x = (23 + √61) / 6:
y'' = 2√61 - 34
Since 2√61 - 34 > 0, the function has a relative minimum at x = (23 + √61) / 6.
For x = (23 - √61) / 6:
y'' = -2√61 - 34
Since -2√61 - 34 < 0, the function has a relative maximum at x = (23 - √61) / 6.
Now, to find the zeros of the function, we set y equal to zero and solve for x:
2x³ - 23x² + 78x - 72 = 0
By using a graphing calculator or numerical methods, we find the zeros of the function as approximately x ≈ -1.5, x ≈ 4.5, and x ≈ 8.
In summary, the relative maximum occurs at x = (23 - √61) / 6, the relative minimum occurs at x = (23 + √61) / 6.
Learn more about Maximum value here
https://brainly.com/question/33411338
#SPJ4
Related Questions
var(x)=e(x^2)-e(x)^2 proof
Answers
We have proved that the expression \(Var(x) = E(x^2) - [E(x)]^2.\)
How to prove the equation?To prove that \(Var(x) = E(x^2) - [E(x)]^2\), where \(Var(x)\) represents the variance of a random variable x and E(x) represents the expected value of x, we can start by using the definition of variance:
\(Var(x) = E[(x - E(x))^2]\)
Expanding the square:
\(Var(x) = E[x^2 - 2x*E(x) + [E(x)]^2]\)
Using linearity of expectations, we distribute the expectation operator:
\(Var(x) = E(x^2) - 2E(x*E(x)) + E([E(x)]^2)\)
Now, let's focus on the term E(x*E(x)). Since E(x) is a constant with respect to the inner expectation operator, we can take it out:
\(E(x*E(x)) = E(x) * E(E(x))\)
The inner expectation, E(E(x)), is just the expected value of a constant, which is equal to that constant:
\(E(E(x)) = E(x)\)
Substituting this back into the equation, we have:
\(Var(x) = E(x^2) - 2E(x*E(x)) + E([E(x)]^2)\)
\(= E(x^2) - 2E(x*E(x)) + E(x^2)\)
Now, consider the term \(E(x*E(x))\). This can be written as:
\(E(x*E(x)) = E(E(x^2|x))\)
This is the conditional expectation of \(x^2\) given x. However, when we take the unconditional expectation E, the conditional expectation collapses to the unconditional expectation of \(x^2\):
\(E(x*E(x)) = E(x^2)\)
Substituting this back into the equation, we get:
\(Var(x) = E(x^2) - 2E(x*E(x)) + E(x^2)\)
\(= E(x^2) - 2E(x^2) + E(x^2)\)
\(= E(x^2) - E(x^2)\)
\(= E(x^2) - [E(x)]^2\)
Hence, we have proved that \(Var(x) = E(x^2) - [E(x)]^2.\)
To know more about Variance
https://brainly.com/question/31432390
#SPJ4
The function f(x) =59(x − 32) can be used to determine the temperature in °C when the temperature is x°F. Find the inverse function that can be used to determine the temperature in °F when the temperature is x°C.
Answers
Answer:
\(F = ( \frac{9}{5}C ) + 32\)
with F = xF and C = xC
=> f(x) = (9/5)x + 32
I'm sorry I can't mark the degree symbol
Step-by-step explanation:
\(f(x) = \frac{5}{9}(x-32) \\xC = \frac{5}{9}(xF-32) \\xC * \frac{9}{5} = \frac{5}{9}(xF-32) * \frac{9}{5} \\xC * \frac{9}{5} + 32 = xF - 32 + 32 \\\\xC * \frac{9}{5} + 32 = xF\)
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answers
Answer:
the numbers of cars pf various colors in a parking lot
Answer: The speed of a car as it changes during a time.
B is the best example of continuous data.
Step-by-step explanation: The contrast between the definitions of continuous data vs. discreet data is that discrete data is counted, continuous data is measured.
A speedometer measures speed continuously, time is measured continuously.
Time can, however, be reported as discreet measurements in situations where that kind of data is needed. (not in this question)
A Number of cars is discreet.
Data from different workers or different days is not continuous.
a type of medicine is given in a 100 miligram dosage. the medicine comes in a 12 gram bottle. how many 100 milligram doses are in a bottle?
Answers
The medicine bottle has 120 doses of 100 miligram each.
As per the known fact, 1000 miligram is 1 gram. So, the amount of medicine in the bottle in milligrams = 12×1000
Performing multiplication on Right Hand Side of the equation
Amount of medicine in bottle = 12000 milligrams.
Now, number of dose of 100 miligram medicine = 1
Amount of dose of 12000 miligram medicine = (1/100)×12000
Performing division and multiplication on Right Hand Side of the equation
Amount of doses in 12000 miligram medicine = 120
Thus, there are 120 doses in a medicine.
Learn more about dosage calculations -
https://brainly.com/question/24793154
#SPJ4
100 POINTS AND BRANLIEST SUPER EASY
For which equation is (4, 3) a solution?
y = x + 3
y = 3 x – 4
y = 2 x – 5
y = 2 x – 1
Answers
Answer:
y = 2 x – 5
Step-by-step explanation:
We can check all of them starting with equation 1.
y = x + 3
3 = 4 + 3
3 = 7
NOT TRUE
Equation 2:
3 = 3(4) - 4
3 = 12 - 4
3 = 8
NOT TRUE
Equation 3:
3 = 2(4) - 5
3 = 8 - 5
3 = 3
TRUE!
This means the last equation is not true.
Please help meeeeeeeeeee !!!!!!!!!!!!!!!!
Answers
There are 7 ounces of applesauce in each container
What is an equation?An equation consists of numbers and variables linked together by mathematical operations to form an expression.
Let x represent the quantity of Newton applesauce
Descartes makes 72.5 ounces of applesauce, which is 2.5 times of Newtons, hence:
2.5x = 72.5
x = 29 ounce
Newton eats 8 ounces, hence:
Remaining = 29 - 8 = 21 ounces
The remaining is placed into 3 containers. If y represent the amount per container:
3y = 21
y = 7 ounces
There are 7 ounces in each container
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
what is 48% of 60? This is for Algebra 1! :)
Answers
Answer:
48% of 60 is 28.8.
hope it helps
if x equal 2 and y eqauls -9 and u ahve to times it what will it be
Answers
Answer:
hey im on here
Step-by-step explanation:
the international average salary income database provides a comparison of average salaries for various professions. the data are gathered from publications and reports obtained directly from government agencies (such as the us bureau of labor statistics) or from the international labour organization. suppose an industrial/organizational psychologist is interested in the relationships between job satisfaction, job performance, and job compensation. she has data from five different countries on the average monthly salaries paid to accountants. she begins her analysis by converting all of the salary data into us dollars:
Answers
To convert the salary data from different countries into US dollars, the industrial/organizational psychologist would need to use the exchange rates between each country's currency and the US dollar. Exchange rates are the value of one currency in terms of another currency.
For example, if the exchange rate between the US dollar and the British pound is 1.38, this means that one US dollar is worth 1.38 British pounds. So, to convert the average monthly salary of an accountant in the UK into US dollars, the psychologist would divide the salary in pounds by the exchange rate.
Once the psychologist has converted all of the salary data into US dollars, she can then compare the average monthly salaries of accountants across the five different countries and analyze the relationships between job satisfaction, job performance, and job compensation.
To know more about average salary refer here:
https://brainly.com/question/28433927
#SPJ11
Solve the equation x² - 7 x=8 .
Answers
Step-by-step explanation:
x=8 and x=-1.It is right answer of this question.
Please help!
Identify the slope of the function: f(x)=2(3x-7)
A:3
B:6
C:7
D:2
Answers
Answer:
The slope is 6
Step-by-step explanation:
f(x)=2(3x-7)
Distribute the 2
f(x)=2*3x-2*7
f(x) = 6x -14
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 6 and the y intercept is -14
The slope is 6
3. Choose 3 Answers.
Which statements are true? Select all true statements.
Answers
The perpendicular line symbols in the diagram indicates that the true statements are;
Plane R is parallel to plane SLine m is perpendicular to both line p and line qThe length \(\overline{EC}\) represents the distance between point E and plane S.What are perpendicular lines?Perpendicular lines are lines that form an angle of 90 degrees with each other.
The plane R and the plane S are both perpendicular to the lines m and n, therefore, the planes R and S will continue indefinitely, maintaining the same distance from each other and the plane R and S are parallel, therefore;
Plane R is parallel to plane SThe lines m and n which are perpendicular to the same planes R and S, indicates that they are perpendicular to the line drawn on the planes, joining the lines. The lines m and n which firm the same corresponding angle to the line joining them indicates that the lines m and n are parallel, and will not eventually intersect.
The drawing indicates the line m is perpendicular to the lines p and q, therefore;
Line m is perpendicular to both line p and line qThe planes R and S are parallel and the lines m and n are also parallel, therefore, the lines joining the lines m and n on both planes and the lengths AD and BC form a parallelogram, such that AB and BC are facing sides of the parallelogram, therefore, AB = BC
The point E is on the line n, and the point C is on the plane S, therefore, the distance \(\overline{EC}\) is the shortest distance from the point E to the plane S, therefore;
The length of \(\overline{EC}\) represents the distance between point E and plane SLearn more on parallel planes here: https://brainly.com/question/1578741
#SPJ1
Explain why the graph above represents a function.
Answers
Simplify. 3.5−4x+2−3x+2x
Answers
Answer:
5.5−5x (sorry if i got it wrong i tried)
Answer:
-5x+5.5
Step-by-step explanation:
3.5−4x+2−3x+2x
-4x-3x+2x+3.5+2
-5x+5.5
a restaurant owner orders new plates and spoons based on the information below.
plates are sold in packages of 9.
spoons are sold in packages of 12.
the restaurant owner orders ab equal number if plates and spoons. What is the least number of packages of plates and packages of spoons she should order to have an equal number of plates and spoons?
Answers
To have an equal number of plates and spoons, the number of plates in packages of 9 must be a multiple of 12 (the number of spoons in packages of 12) and the number of spoons in packages of 12 must be a multiple of 9 (the number of plates in packages of 9).
The least common multiple of 9 and 12 is 36. Therefore, the restaurant owner should order packages of plates and spoons such that the number of plates is a multiple of 4 and the number of spoons is a multiple of 3, in order to have an equal number of plates and spoons. The smallest number of packages of plates and spoons that satisfies this condition is one package of plates (9 plates) and one package of spoons (12 spoons). This gives a total of 9 plates and 12 spoons, which are equal in number. Therefore, the restaurant owner should order at least one package of plates and one package of spoons to have an equal number of plates and spoons.
Learn more about packages here
https://brainly.com/question/8179427
#SPJ11
I need help asap please
Answers
Answer:
i don't know
Step-by-step explanation:
how to solve that
Estimate the area under the graph of f(x)=x^2+x+1 over the intervat [1,5] using five approximating rectangles and right endpoints.
Rn=
Repeat the approximation using left endpoints.
Ln=
Answers
Estimate the area under the graph of f(x) over interval [1, 5] using five approximating rectangles and right endpoints. Use formula Δx × f(x) to find the area of each rectangle. The Riemann Sum for the function using right endpoints is 76.08 square units, and the Riemann Sum for the function using left endpoints is 34.72 square units.
Here, we need to Estimate the area under the graph of f(x) = x² + x + 1 over the interval [1, 5] using five approximating rectangles and right endpoints.
The area of each rectangle can be calculated by the formula,Δx × f(x)We have to break the interval [1, 5] into five intervals,Δx = (b - a) / nΔx = (5 - 1) / 5Δx = 4 / 5
= 0.8
We know that the value of f(x) = x² + x + 1
Therefore, the values of f(x) for the respective x-values are:
f(1) = 1² + 1 + 1 = 3f(1.8) = (1.8)² + 1.8 + 1
= 6.24f(2.6)
= (2.6)² + 2.6 + 1
= 12.56f(3.4)
= (3.4)² + 3.4 + 1
= 21.16f(4.2)
= (4.2)² + 4.2 + 1
= 32.84
Now, we will find the Riemann Sum for the given function using right endpoints.
Rn = f(x1) Δx + f(x2) Δx + f(x3) Δx + f(x4) Δx + f(x5) Δx
= [f(1) + f(1.8) + f(2.6) + f(3.4) + f(4.2)] Δx
= [3 + 6.24 + 12.56 + 21.16 + 32.84] × 0.8
= 76.08 square units
Repeat the approximation using left endpoints.Ln = f(x0) Δx + f(x1) Δx + f(x2) Δx + f(x3) Δx + f(x4) Δx
= [f(1) + f(1.8) + f(2.6) + f(3.4) + f(4.2)]
Δx= [3 + 4.84 + 8.36 + 13.96 + 22.44] × 0.8
= 34.72 square units
Therefore, Rn = 76.08 square units and Ln = 34.72 square units.
To know more about area under the graph Visit:
https://brainly.com/question/30211849
#SPJ11
can 16/x be expressed as x^-16
Answers
Answer:no
Step-by-step explanation:
for example Exponents are numbers that have been multiplied by themselves. For instance, 3 · 3 · 3 · 3 could be written as the exponent 34
The cost to rent a moving truck is a flat fee of $25 plus $0.60 per mile. The equation e = 25 +0.6m models the cost, e,
in dollars for the number of miles, m, traveled in the truck.
Identify the independent and dependent variables.
Answers
Answer:
The independent variable is m (the number of miles driven), and the dependent variable is "e" (the cost)
Step-by-step explanation:
Notice that the cost "depends" upon the number of miles driven, therefore, the cost (identified with the letter "e") is the dependent variable which depends upon the number of miles driven (and which is the independent variable identified with the letter "m")
Answer: The independent variable is m (number of miles) and the dependent variable is e (the cost).
Step-by-step explanation:
In this situation, if you were to graph the equation on the number line ,
M will be the x and e will be the y.And we know most of the time that x is independent in that situations and y is dependent.
The cost of depends on how many miles travelled.If the cost will go up it depends on how many miles.
What is the solution to the system below?
x + y = 5
x - y = 3
Answers
( x, y ) = ( 4, 1 )
hope it helps!
Answer:
x= 4
y= 1
Step-by-step explanation:
by adding 2 equations
2x = 8
x= 4
by sub. in Equation 1
4+y=5
y = 5-4
y= 1
WILL MARK BRAINLIEST!!!!!
MUSIC Carla downloaded some songs onto her digital music player and now the player is 5/6 full. If the player was 1/5 full before the download, what fraction of the space on the player do the new songs occupy?
Answers
Answer:
19
Step-by-step explanation:
You have to convert the fractions to a equivalent fraction. 5/6 to 25/30. 1/5 to 6/30. Then you do 25/30 - 6/30 which gives you 19/30.
Graph f(x)=-0.25x+4 I need it asap the graph only goes up to 10
Answers
Answer: The exact points are (0,4) and (4,3)
Step-by-step explanation: f(x) is the same thing as using the variable y. You can plug in numbers for the x variable and evaluate. For example, you can use the numbers 0 and 4 for x. 0.25 times 0+4 =4. (0,4) and -0.25 times 4+4=3. (4,3)
Please help, Factored form
Answers
Answer:
B
Step-by-step explanation:
Factored form means it is broken down into the expressions you would multiply to get the answer
Answer:
B. ( 2x +3)(x-5)
Explanation:
A fully factored form means the given number or polynomial is expressed as a product of the simplest possible form.
Which of the following is true?
Answers
\(▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)
The Correct choice is A :
RT is an altitude of Triangle QRSAnswer:
A, because ∆ QRS isn't a right angled triangle unlike the other choices and its height is in the middle,the rest of the choices are right angled and the line segments in the choice are all their hypotenuse,and the hypotenuse of a triangle isn't it's height
Find the inequality represented by the graph.
Answers
Answer:
y= -1/3x+1
Step-by-step explanation:
Why is 3 root not a polynomial?
Answers
A mathematical expression with coefficients and variables is called a polynomial. The polynomial 3 root is not one because of the non-integer, irrational exponent (the root of 3).
A mathematical expression with coefficients and variables is called a polynomial. A nxn + a (n-1)x(n-1) +... + a 2x2 + a 1x + a 0 can be used to represent the formula, where n is an integer and an I are constants. The polynomial 3 root is not one because of the non-integer, irrational exponent (the root of 3). The polynomial 3(1/2) cannot be one since the exponent (1/2) is not an integer. As a result, 3 root cannot be expressed as a polynomial.
Learn more about polynomial here
https://brainly.com/question/11536910
#SPJ4
Fernando purchased 1 pound of dried cranberries and 4 pounds of almonds to make a trail mix. Cranberries cost $4 per pound and almonds cost $5 per pound. What is the price per pound of the trail mix? $
Answers
Answer:
$24
Step-by-step explanation:
Cranberries needed: 1 pound
Cost of 1 pound = $4
Almonds needed: 4 pound
Cost of 1 pound = $5
4 x 5 = $20
20 + 4 = $24
Answer:
4.80
Step-by-step explanation:
What is the volume of the sphere? Round your answer to the nearest tenth
Answers
Answer:
523.6 ft
Step-by-step explanation:
Answer:
523.6 ft
Step-by-step explanation:
Q1. A heavy general purpose truck costs $12,000 has a life of six years with a $2,000 SV. using the
MACRS with a GDS recovery period of five years. What is the BV of the equipment at the end of
(including) year four?
IN EXCEL WITH EXPLANATION PLEASE
Answers
Answer:
Therefore, the book value of the equipment at the end of year four (including year four) is $2,880.
Step-by-step explanation:
To calculate the book value of the equipment at the end of year four using the MACRS method with GDS recovery period of five years, we can use the following steps in Excel:
1. Open a new Excel spreadsheet and create the following headers in row 1: Year, Cost, Depreciation Rate, Annual Depreciation, Cumulative Depreciation, and Book Value.
2. Fill in the Year column with the years 1 through 6 (since the truck has a life of six years).
3. Enter the cost of the truck, $12,000, in cell B2.
4. Use the following formula in cell C2 to calculate the depreciation rate for each year:
=MACRS.VDB(B2, 5, 5, 1, C1)
This formula uses the MACRS.VDB function to calculate the depreciation rate for each year based on the cost of the truck (B2), the GDS recovery period of five years, the useful life of six years, the salvage value of $2,000, and the year (C1).
5. Copy the formula in cell C2 and paste it into cells C3 through C7 to calculate the depreciation rate for each year.
6. Use the following formula in cell D2 to calculate the annual depreciation for each year:
=B2*C2
This formula multiplies the cost of the truck (B2) by the depreciation rate for each year (C2) to get the annual depreciation.
7. Copy the formula in cell D2 and paste it into cells D3 through D7 to calculate the annual depreciation for each year.
8. Use the following formula in cell E2 to calculate the cumulative depreciation for each year:
=SUM(D$2:D2)
This formula adds up the annual depreciation for each year from D2 to the current row to get the cumulative depreciation.
9. Copy the formula in cell E2 and paste it into cells E3 through E7 to calculate the cumulative depreciation for each year.
10. Use the following formula in cell F2 to calculate the book value of the equipment for each year:
=B2-E2
This formula subtracts the cumulative depreciation for each year (E2) from the cost of the truck (B2) to get the book value.
11. Copy the formula in cell F2 and paste it into cells F3 through F7 to calculate the book value for each year.
12. The book value of the equipment at the end of year four (including year four) is the value in cell F5, which should be $2,880.
The graph shows the cost of purchasing T-shirts. Find the constant rate of change for the graph. Then explain what points (0,0) and (1,9) represent
Answers
Answer:
See below
Step-by-step explanation:
As per the attached graph we observe that the constant rate of change is 9 as each step of horizontal change corresponds to 9 steps of vertical change
It is found as the division below:
(9-0)/(1-0) = 9/1 = 9Point (0, 0) indicates the start point
Point (1, 9) indicates the cost of 1 t-shirt
As to the attachment graph ;
we observed that the constant rate is 9each step of horizontal change correspond to 9 steps of vertical changeNow,
according to the question
it is found as the division below ;
(9-0)/(1-0)=9/1 = 9the point which is indicating the starting point ;
(0,0)the point which indicate the cost of one t-shirt ;
(1,9)