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Stewart_Calc_7ET ch04sec03
MULTIPLE CHOICE
1. Determine where the graph of the function is concave upward and where it
is concave downward. Also, find all inflection points of the function.
a.
CU on , CD on ,
IP
b.
CU on , CD on ,
IP
c.
CU on , CD on ,
IP
d.
CU on , CD on ,
IP
2. Determine where the graph of the function is concave upward and
where it is concave downward. Also, find all inflection points of the function.
a.
CU on ,
IP none
b.
CU on and , CD on ,
IP and
c.
CD on ,
IP none
d.
CU on , CD on and ,
IP and
3. Determine where the graph of is concave upward and where it is concave
downward. Also, find all inflection points of the function.
a.
concave downward: and , concave upward: and ;
inflection points: and
b.
concave downward: and , concave upward: and ;
inflection points: and
c.
concave downward: and , concave upward: nowhere; inflection
points: none
d.
concave downward: nowhere, concave upward: and ; inflection
points: none
4. Use the Second Derivative Test to find the relative extrema, if any, of the function
.
a.
Rel. max. ,
rel. min.
b.
Rel. max. ,
rel. min.
c.
Rel. max. ,
rel. min.
d.
Rel. max. ,
rel. min.
5. Find the relative extrema, if any, of . Use the Second Derivative Test, if
possible.
a.
relative minimum: none, relative maximum:
b.
relative minimum: , relative maximum: none
c.
relative minimum: , relative maximum: none
d.
relative minimum: none, relative maximum:
6. Find the relative extrema, if any, of . Use the Second Derivative Test, if
possible.
a.
relative minimum: none, relative maximum:
b.
relative minimum: , relative maximum: none
c.
relative minimum: none, relative maximum:
d.
relative minimum: , relative maximum: none
7. Find the point(s) of inflection of the graph of
a.
, , and
b.
c.
d.
8. How many points of inflection are on the graph of the function?
a.
5
b.
2
c.
3
d.
4
e.
1
9. Find the inflection points for the function given.
,
a.
,
b.
,
c.
,
d.
,
e.
,
10. The graph of the derivative of a continuous function f is shown. On what intervals is f
decreasing?
.
a.
b.
c.
d.
e.
None of these
11. 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.
a.
(a) Increasing and
decreasing on
(b) Rel. max at , rel. min. at
2 4 6 8 10–2–4–6–8–10 x
y
b.
(a) Increasing and
decreasing on
(b) Rel. min. at
c.
(a) Increasing ,
decreasing on
(b) Rel. min at 0
d.
(a) Increasing ,
decreasing on
(b) Rel. min at
12. 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
(b) Rel. min.
b.
(a) Increasing on ,
decreasing on
(b) Rel. max.
c.
(a) Increasing on ,
decreasing on
(b) Rel. min.
d.
(a) Increasing on ,
decreasing on
(b) Rel. max.
13. 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 and decreasing on
(b) Rel. max. ,
rel. min.
b.
(a) Increasing on and decreasing on
(b) Rel. max. ,
rel. min.
c.
(a) Increasing on , decreasing on and
(b) Rel. max. ,
rel. min.
d.
(a) Increasing on , decreasing on and
(b) Rel. max. ,
rel. min.
14. 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
(b) Rel. min.
b.
(a) Increasing on
(b) None
c.
(a) Increasing on ,
decreasing on
(b) Rel. max.
d.
(a) Decreasing on
(b) None
15. 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 and 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
(b) Rel. max. ,
rel. min.
d.
(a) Increasing on , decreasing on and
(b) Rel. max. ,
rel. min.
16. Find the intervals where is increasing and where it is decreasing.
a.
increasing: , decreasing:
b.
increasing: , decreasing:
c.
increasing: , decreasing:
d.
increasing: , decreasing:
17. Determine where the graph of the function is concave upward and where it
is concave downward. Also, find all inflection points of the function.
a.
CU on , CD on and
IP and
b.
CU on , CD on ,
IP
c.
CU on , CD on ,
IP
d.
CU on , CD on ,
IP
18. Find the maximum or minimum point(s) of the function.
a.
b.
c.
d.
e.
MULTIPLE RESPONSE
1. The graph of the first derivative of a function f is shown below. At what values of
x does f have a local maximum or minimum?
a.
9
b.
3
c.
10
d.
8
e.
4
f.
7
NUMERIC RESPONSE
1. Find a cubic function that has a local maximum value of at 1
and a local minimum value of –1,184 at 7.
2. The graph of the first derivative of a function f is shown below. At what values of x
does f have a local maximum or minimum?
3. The graph of the second derivative of a function f is shown. State the x-
coordinates of the inflection points of f.
4. Estimate the extreme values of the function. Round the answers to the nearest hundredth.
SHORT ANSWER
1. You are given the graph of a function f.
(a) Determine the intervals on which f is increasing or decreasing.
(b) Find the relative maxima and relative minima of f, if any.
2. Given .
(a) Find the intervals on which f is increasing or decreasing.
(b) Find the relative maxima and relative minima of f.
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
3. Given .
(a) Find the intervals on which f is increasing or decreasing.
(b) Find the relative maxima and relative minima of f.
4. Consider the function . (a) Find the intervals on which f is increasing or
decreasing. (b) Find the relative maxima and relative minima of f.
5. Consider the function . (a) Find the intervals on which f is increasing or
decreasing. (b) Find the relative maxima and relative minima of f.
6. You are given the graph of a function f. Determine the intervals where the graph of f is
concave upward and where it is concave downward. Find all inflection points of f.
7. You are given the graph of the second derivative of a function f. (a) Determine the
intervals where the graph of f is concave upward and where it is concave downward. (b)
Find the x-coordinates all inflection points of f.
8. Determine where the graph of the function
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
is concave upward and where it is concave downward. Also, find all inflection points of
the function.
9. Determine where the graph of the function is concave upward and where it is
concave downward on the interval . Also, find all inflection points of the
function.
10. Determine where the graph of is concave upward and where it is concave
downward. Also, find all inflection points of the function.
