Stewart – Calculus 8e ET Chapter 4 Form D
____ 3. Find the intervals where is increasing and where it is decreasing.
a. increasing: , decreasing:
b. increasing: , decreasing:
c. increasing: , decreasing:
d. increasing: , decreasing:
____ 4. Let P (x) and Q (x) be polynomials. Find
if the degree of P (x) is 2 and the degree of Q (x) is 6.
a. 9
b. 5
c. – 4
d. 0
e. 4
____ 5. Find the limit.
a.
b.
c.
d.
Stewart – Calculus 8e ET Chapter 4 Form D
____ 6. A skydiver leaps from a helicopter hovering high above the ground. Her velocity t sec later and
before deploying her parachute is given by
where is measured in meters per second. What is her terminal velocity? Hint: Evaluate
a. 54 m/sec
b. 8.1 m/sec
c. 87 m/sec
d. 62.1 m/sec
____ 7. Evaluate the limit.
a. 9
b. 0
c. –9
d.
2
9
____ 8. Evaluate the limit using l’Hôpital’s Rule.
a. 6
b. –6
c. 12
d. 27
Stewart – Calculus 8e ET Chapter 4 Form D
____ 9. Evaluate the limit.
a. 2
b.
c. 0
d.
e.
____ 10. Evaluate the limit.
a. –5
b.
c.
d. 1
e. 0
____ 11. Find the limit.
a.
b.
c.
d. 5
e. 0
Stewart – Calculus 8e ET Chapter 4 Form D
____ 12. Find the slant asymptote of the graph of using the curve-sketching guidelines.
a.
246–2–4–6–8–10–12 x
2
4
6
8
10
12
14
–2
–4
y
c.
2 4 6 8 10 12–2–4–6 x
2
4
6
8
10
12
14
–2
–4
y
b.
246–2–4–6–8–10–12 x
2
4
–2
–4
–6
–8
–10
–12
–14
y
d.
2 4 6 8 10 12–2–4–6 x
2
4
–2
–4
–6
–8
–10
–12
–14
y
____ 13. What can you say about point of inflation for ?
a. point of inflation goes away from the origin
b. point of inflation goes away from
c. point of inflation gets closer to the origin
d. point of inflation gets closer to
Stewart – Calculus 8e ET Chapter 4 Form D
____ 14. Identify any transitional values of at which the basic shape of the curve changes.
a.
b.
c.
d.
____ 15. Find two positive numbers whose product is and whose sum is a minimum.
a. 6, 24
b. 2, 72
c.
d. 3, 48
e.
____ 16. A rectangular beam will be cut from a cylindrical log of radius inches. Suppose that the
strength of a rectangular beam is proportional to the product of its width and the square of its
depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log.
a. in, in
b. in, in
c. in, in
d. in, in
e. in, in
Stewart – Calculus 8e ET Chapter 4 Form D
____ 17. Find the dimensions of the rectangle enclosed in the semicircle with the largest
possible area.
4812–4–8–12 x
4
8
12
–4
–8
–12
y
a. in. in.
b. 5 in. 7 in.
c. in. in.
d. in. in.
____ 18. A manufacturer has been selling 1,200 television sets a week at $400 each. A market survey
indicates that for each $30 rebate offered to the buyer, the number of sets sold will increase by 60
per week. Find the demand function.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 4 Form D
____ 19. The size of the monthly repayment k that amortizes a loan of A dollars in N years at an interest rate
of r per year, compounded monthly, on the unpaid balance is given by
The value of r can be found by performing the iteration
A family secured a loan of $360,000 from a bank to finance the purchase of a house. They have
agreed to repay the loan in equal monthly installments of $2342 over 25 years. Find the interest
rate on this loan. Round the rate to one decimal place.
a. 4.1%
b. 5.1%
c. 6.1%
d. 7.1%
____ 20. Find f.
,
a.
b.
c.
d.
e. None of these
Stewart – Calculus 8e ET Chapter 4 Form D
Answer Key
Stewart – Calculus 8e ET Chapter 4 Form E
____ 1. Find the critical number(s), if any of the function Select the correct answer.
a.
b.
c. 0,
d. 0,
____ 2. Find the critical number(s), if any, of the function . Select the correct answer.
a.
10
b.
5
c.
10
and
10
d.
5
and
5
3. Find the absolute maximum and absolute minimum values, if any, of the function
on [0, 9]
4. Find the critical number(s) of the function.
____ 5. Use the Second Derivative Test to find the relative extrema, if any, of the function
. Select the correct answer.
a. Rel. max. ,
rel. min.
b. Rel. max. ,
rel. min.
c. Rel. max. ,
rel. min.
d. Rel. max. ,
rel. min.
6. How many points of inflection are on the graph of the function?
Stewart – Calculus 8e ET Chapter 4 Form E
7. Given .
(a) Find the intervals on which f is increasing or decreasing.
(b) Find the relative maxima and relative minima of f.
8. Find the limit.
____ 9. A skydiver leaps from a helicopter hovering high above the ground. Her velocity t sec later and
before deploying her parachute is given by
where is measured in meters per second. What is her terminal velocity? Hint: Evaluate
Select the correct answer.
a. 54 m/sec
b. 7 m/sec
c. 47 m/sec
d. 87 m/sec
10. Evaluate the limit using l’Hôpital’s Rule.
____ 11. Evaluate the limit. Select the correct answer.
a. –2
b.
1
c. 0
d. 2
12. Sketch the graph of the function using the curve-sketching guidelines.
Stewart – Calculus 8e ET Chapter 4 Form E
____ 13. What is the shortest possible length of the line segment that is cut off by the first quadrant and is
tangent to the curve at some point? Select the correct answer.
a.
26
b.
c.
d.
e. None of these
14. Find two positive numbers whose product is and whose sum is a minimum.
15. A rectangular storage container with an open top is to have a volume of 10 . The length of its
base is twice the width. Material for the base costs $12 per square meter. Material for the sides
costs $5 per square meter. Find the cost of materials for the cheapest such container.
____ 16. A production editor decided that a promotional flyer should have a 1-in. margin at the top and the
bottom, and a -in. margin on each side. The editor further stipulated that the flyer should have
an area of 72 . Determine the dimensions of the flyer that will result in the maximum printed
area on the flyer. Select the correct answer.
a. 6 in. 12 in.
b. 3 in. 24 in.
c. in. in.
d. in. in.
17. Consider the following problem: A farmer with ft of fencing wants to enclose a rectangular
area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the
largest possible total area of the four pens?
Stewart – Calculus 8e ET Chapter 4 Form E
18. Use Newton’s method to approximate the zero of between and
using . Continue until two successive approximations differ by less than 0.00001.
____ 19. Find f. Select the correct answer.
,
a.
b.
c.
d.
e. None of these
20. A particle is moving with the given data. Find the position of the particle.
,
Stewart – Calculus 8e ET Chapter 4 Form E
Answer Key
Stewart – Calculus 8e ET Chapter 4 Form F
____ 1. Find the critical number(s), if any, of the function . Select the correct answer.
a.
10
b.
5
c.
10
and
10
d.
5
and
5
2. Find the absolute maximum and absolute minimum values, if any, of the function
on [0, 9]
3. You are given the graph of the derivative of a function f.
(a) Determine the intervals on which f is increasing or decreasing.
(b) Find the x-coordinate of the relative maxima and relative minima of f.
246810–2–4–6–8–10 x
y
4. Given .
(a) Find the intervals on which f is increasing or decreasing.
(b) Find the relative maxima and relative minima of f.
Stewart – Calculus 8e ET Chapter 4 Form F
____ 5. Given .
(a) Find the intervals on which f is increasing or decreasing.
(b) Find the relative maxima and relative minima of f.
a. (a) Increasing on , decreasing on and
(b) Rel. max. ,
rel. min.
b. (a) Increasing on and decreasing on and
(b) Rel. max. ,
rel. min.
c. (a) Increasing on and , decreasing on and
(b) Rel. max. ,
rel. min.
d. (a) Increasing on and , decreasing on
(b) Rel. max. ,
rel. min.
6. A skydiver leaps from a helicopter hovering high above the ground. Her velocity t sec later and
before deploying her parachute is given by
where is measured in meters per second. What is her terminal velocity? Hint: Evaluate
7. Evaluate the limit using l’Hôpital’s Rule.
8. Find the limit.
9. Sketch the curve.
Stewart – Calculus 8e ET Chapter 4 Form F
____ 10. Find the slant asymptote of the function . Select the correct answer.
a.
b.
c.
d.
e.
11. Sketch the graph of the function using the curve-sketching guidelines.
____ 12. Sketch the graph of the function using the curve-sketching guidelines.
a.
12345678x
1
–1
–2
–3
–4
y
c.
–1–2–3–4–5–6 x
1
2
3
4
–1
–2
–3
–4
y
b.
–1–2–3–4–5–6 x
1
2
3
4
–1
–2
–3
–4
y
d.
12345678x
1
2
3
4
5
–1
y
Stewart – Calculus 8e ET Chapter 4 Form F
13. What can you say about point of inflation for ?
14. a) Graph the funtion .
b) Use l’Hospitals’ rule to explain the behavior as
____ 15. Find two positive numbers whose product is and whose sum is a minimum.
Select the correct answer.
a.
b. 3, 48
c. 6, 24
d.
e. 2, 72
16. A rectangular storage container with an open top is to have a volume of 10 . The length of its
base is twice the width. Material for the base costs $12 per square meter. Material for the sides
costs $5 per square meter. Find the cost of materials for the cheapest such container.
17. Find the point on the line that is closest to the origin.
18. A rectangular beam will be cut from a cylindrical log of radius inches. Suppose that the
strength of a rectangular beam is proportional to the product of its width and the square of its
depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log.
Stewart – Calculus 8e ET Chapter 4 Form F
19. Find the dimensions of the rectangle enclosed in the semicircle with the largest
possible area.
4812–4–8–12 x
4
8
12
–4
–8
–12
y
____ 20. A manufacturer has been selling 1,200 television sets a week at $400 each. A market survey
indicates that for each $30 rebate offered to the buyer, the number of sets sold will increase by 60
per week. Find the demand function. Select the correct answer.
a.
b.
c.
d.
e.