Stewart – Calculus 8e ET Chapter 4 Form F
Answer Key
Stewart – Calculus 8e ET Chapter 4 Form F
Stewart – Calculus 8e ET Chapter 4 Form G
____ 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 critical number(s) of the function. Select the correct answer.
a.
b.
c.
d.
e.
3. For what values of c does the curve have maximum and minimum points?
4. Find the point(s) of inflection of the graph of
____ 5. Find the inflection points for the function given. Select the correct answer.
,
a. ,
b. ,
c. ,
d. ,
e. ,
Stewart – Calculus 8e ET Chapter 4 Form G
6. The graph of the derivative of a continuous function f is shown. On what intervals is f
decreasing?
.
____ 7. Find the limit. Select the correct answer.
a. 0
b.
c.
d.
e. 1
8. Find the limit.
Stewart – Calculus 8e ET Chapter 4 Form G
9. What is the function of the graph?
10. Sketch the graph of the function using the curve-sketching guidelines.
11. Sketch the graph of the function using the curve-sketching guidelines.
Stewart – Calculus 8e ET Chapter 4 Form G
____ 12. What is the function of the graph? Select the correct answer.
a.
b.
c.
d.
e.
13. Find two positive numbers whose product is and whose sum is a minimum.
____ 14. Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius
. Select the correct answer.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 4 Form G
15. 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
____ 16. An apple orchard has an average yield of 32 bushels of apples per tree if tree density is 30 trees per
acre. For each unit increase in tree density, the yield decreases by 2 bushels per tree. How many
trees per acre should be planted to maximize yield? Select the correct answer.
a. 27 trees/acre
b. 30 trees/acre
c. 37 trees/acre
d. 23 trees/acre
____ 17. Use Newton’s method to obtain an approximation to the root of to within 0.00001.
Select the correct answer.
a. 0.62821
b. 0.48918
c. 0.56127
d. 0.51493
18. Find f.
,
Stewart – Calculus 8e ET Chapter 4 Form G
____ 19. Given that the graph of f passes through the point (4, 69) and that the slope of its tangent line at
is , find f (1) . Select the correct answer.
a. –4.5
b. 8
c. 12
d. 11
e. 1
20. Find the critical number(s), if any, of the function .
Stewart – Calculus 8e ET Chapter 4 Form G
Answer Key
Stewart – Calculus 8e ET Chapter 4 Form G
Stewart – Calculus 8e ET Chapter 4 Form H
1. Estimate the extreme values of the function.
____ 2. Find the critical number(s), if any, of the function Select the correct answer.
a.
b. –3
c.
d.
3. Verify that the function satisfies the three hypotheses of Rolle’s Theorem on the given interval.
Then find all numbers c that satisfy the conclusion of Rolle’s Theorem.
4. Determine where the graph of is concave upward and where it is concave
downward. Also, find all inflection points of the function.
5. The graph of the derivative of a continuous function f is shown. On what intervals is f
decreasing?
.
Stewart – Calculus 8e ET Chapter 4 Form H
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. Select the correct answer.
a.
1
42
b.
13
42
c.
1
42
d.
1
2
8. Evaluate the limit.
9. Use l’Hospital’s Rule to calculate the exact value of the limit as
10. Find the limit.
Stewart – Calculus 8e ET Chapter 4 Form H
11. Sketch the graph of the function using the curve-sketching guidelines.
12. Sketch the graph of the function using the curve-sketching guidelines.
Stewart – Calculus 8e ET Chapter 4 Form H
____ 13. Select the correct graph for the given function .
Select the correct answer.
a.
1234–1–2–3–4
2
4
6
8
10
–2
–4
–6
–8
–10
d.
1234–1–2–3–4
2
4
6
8
10
–2
–4
–6
–8
–10
b.
1234–1–2–3–4
2
4
6
8
10
–2
–4
–6
–8
–10
e.
1234–1–2–3–4
2
4
6
8
10
–2
–4
–6
–8
–10
c.
1234–1–2–3–4
2
4
6
8
10
–2
–4
–6
–8
–10
Stewart – Calculus 8e ET Chapter 4 Form H
____ 14. 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.
b.
c.
d.
42
e. None of these
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. 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.
Stewart – Calculus 8e ET Chapter 4 Form H
____ 17. Use Newton’s method to approximate the zero of between and
using . Continue until two successive approximations differ by less than 0.00001.
Select the correct answer.
a. 0.55341
b. 0.52221
c. 0.48751
d. 0.45061
18. Evaluate , and tell whether its antiderivative F is increasing or decreasing at the
point radians.
____ 19. Find f.
Select the correct answer.
a.
b.
c.
d.
e.
20. Given that the graph of f passes through the point (4, 69) and that the slope of its tangent line at
is , find f (1) .
Stewart – Calculus 8e ET Chapter 4 Form H
Answer Key
Stewart – Calculus 8e ET Chapter 4 Form H