TUTOR DANIEL
phaoun
math_step_step-2.docxFai 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
