Find the relative extrema of the function if they exist

Fai alshammari

Chapter 2

Section 2.1

Q1:- Consider the graph to the right. Explain the idea of a critical value. Then determine which​ x-values are critical​ values, and state why.

Q2:-

Find the relative extreme points of the​ function, if they exist. Then sketch a graph of the function.

​f(x)equals=x squared plus 6 x plus 15x2+6x+15

Q3:-

Find the relative extreme points of the​ function, if they exist. Then sketch a graph of the function.

​G(x)equals=x cubed minus 9 x squared plus 1x3−9x2+1

· Identify all the relative minimum points. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice

· Identify all the relative maximum points. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

·

· Graph the function. Choose the correct graph below.

SECTION 2.2

Q1:-

Find all relative extrema and classify each as a maximum or minimum. Use the​ second-derivative test where possible.

f(x)equals=negative 27 x cubed plus 9 x plus 2−27x3+9x+2

_Identify all the relative minima. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

_Identify all the relative maxima. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice

Q2:-

Sketch the graph of the following function. List the coordinates of where extrema or points of inflection occur. State where the function is increasing or decreasing as well as where it is concave up or concave down.

f left parenthesis x right parenthesisf(x)equals=x Superscript 4 Baseline minus 4 x cubed plus 3x4−4x3+3

_What are the coordinates of the relative​ extrema? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

_Identify all the relative maxima. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

_On what​ interval(s) is f increasing or​ decreasing?

_On what​ interval(s) is f concave up or concave​ down?

_ SKETCH GRAPH

Q3:-

Sketch the graph that possesses the characteristics listed.

f is concave

up at

​(negative 1−1​,66​),

concave

downdown

at

​(77​,negative 4−4​),

and has an inflection point at left parenthesis 3 comma 1 right parenthesis .(3,1).

SECTION 2.3

Q1:-

Determine the vertical​ asymptote(s) of the following function. If none​ exist, state that fact.

​f(x)equals=StartFraction x plus 3 Over x squared plus 9 x plus 18 EndFractionx+3x2+9x+18

Q2:-

Determine the horizontal asymptote of the function.

​f(x)equals=StartFraction 8 x cubed minus 8 x plus 3 Over 10 x cubed plus 4 x minus 7 EndFraction8x3−8x+310x3+4x−7

Q3:-

Sketch the graph of the function. Indicate where each function is increasing or​ decreasing, where any relative extrema​ occur, where asymptotes​ occur, where the graph is concave up or concave​ down, where any points of inflection​ occur, and where any intercepts occur.

​f(x)equals=StartFraction x plus 10 Over x squared minus 100 EndFractionx+10x2−100

_ REST OF QUESTIONS ARE ON SECTION 2.3 QUESTION 3

SECTION 2.4

Q1: Find the absolute maximum and minimum values of the function over the indicated​ interval, and indicate the​ x-values at which they occur.

f left parenthesis x right parenthesis equals 7 plus 5 x minus 5 x squaredf(x)=7+5x−5x2​;

left bracket 0 comma 4 right bracket[0,4]

Q2:

Find the absolute maximum and minimum values of the function over the indicated​ interval, and indicate the​ x-values at which they occur.

f left parenthesis x right parenthesisf(x)equals=x cubed minus 6 x squaredx3−6x2​;

left bracket 0 comma 8 right bracket[0,8]-

Q3:

Find the absolute maximum and minimum values of the function over the indicated​ interval, and indicate the​ x-values at which they occur.

f left parenthesis x right parenthesis equals left parenthesis x plus 4 right parenthesis Superscript two thirds Baseline minus 2f(x)=(x+4)23−2​;

left bracket negative 6 comma 5 right bracket[−6,5]

Q4:

Find the absolute maximum and minimum values of the​ function, if they​ exist, over the indicated interval. Also indicate the​ x-value at which each extremum occurs.

f left parenthesis x right parenthesisf(x)equals=one third x cubed minus 3 x13x3−3x​;

left bracket negative 2 comma 2 right bracket[−2,2]

SECTION 2.5

Q1: Of all numbers whose difference is

88​,

find the two that have the minimum product.

Q2: A carpenter is building a rectangular shed with a fixed perimeter of

4848

ft. What are the dimensions of the largest shed that can be​ built? What is its​ area?

Q3:

Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that​ revenue,

Upper R left parenthesis x right parenthesisR(x)​,

and​ cost,

Upper C left parenthesis x right parenthesisC(x)​,

of producing x units are in dollars.

Upper R left parenthesis x right parenthesisR(x)equals=4 x4x​,

Upper C left parenthesis x right parenthesisC(x)equals=0.05 x squared plus 0.7 x plus 10.05x2+0.7x+1

Q4: A university is trying to determine what price to charge for tickets to football games. At a price of

​$2222

per​ ticket, attendance averages

40 comma 00040,000

people per game. Every decrease of

​$22

adds

10 comma 00010,000

people to the average number. Every person at the game spends an average of

​$3.003.00

on concessions. What price per ticket should be charged in order to maximize​ revenue? How many people will attend at that​ price?

SECTION 2.6\

Q1:

Let​ R(x), C(x), and​ P(x) be,​ respectively, the​ revenue, cost, and​ profit, in​ dollars, from the production and sale of x items. If

​R(x)equals=88x

and

​C(x)equals=0.001 x squared plus 1.9 x plus 400.001x2+1.9x+40​,

find each of the following.

​a)​ P(x)

b)

​ R(200200​),

​C(200200​),

and

​P(200200​)

c)

Upper R primeR​(x),

Upper C primeC​(x),

and

Upper P primeP​(x)

​d)

Upper R primeR​(200200​),

Upper C primeC​(200200​),

and

Upper P primeP​(200200​)

Q2:-

A particular computing company finds that its weekly​ profit, in​ dollars, from the production and sale of x laptop computers is

​P(x)equals=negative 0.006 x cubed minus 0.3 x squared plus 600 x minus 800−0.006x3−0.3x2+600x−800.

Currently the company builds and sells

99

laptops weekly.

​a)

What is the current weekly​ profit?

​b)

How much profit would be lost if production and sales dropped to

88

laptops​ weekly?

​c)

What is the marginal profit when

xequals=99​?

​d)

Use the answer from part​ (a)-(c) to estimate the profit resulting from the production and sale of

1010

laptops weekly.

Q3:- Assume that​ R(x) is in dollars and x is the number of units produced and sold. For the​ total-revenue function

​R(x)equals=7 x7x​,

find

Upper DeltaΔR

and

Upper R primeR​(x)

when

xequals=4040

and

Upper DeltaΔxequals=11.

Q4: on site

Q5: on site

Section 2.7

Q1 on site

Q2 on site

Section 2.8

Q1 , q2 , q3 , q4 all on site