Curve Sketching 2
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. What are the possible values for
if
exists and
for every
a.
c.
b.
d.
____ 2. If
for all , then
a.
c.
for every
for every
b.
d.
for every
for every
____
____
____
____
3. What is the behaviour of
if
a. Increasing
b. Stationary
4. If
is decreasing for every
a.
b.
5. Let
a.
b.
6. Let
?
c. Decreasing
d. Need more information
, then which choice is not a possibility for
c.
d.
for
a. horizontal asymptote
b. vertical asymptote
?
. What is the equation of the horizontal asymptote of
b.
approach the asymptote as
c.
tends to
. For what value(s) of
, from below
does
have a point of inflection?
f '( x)
–4
a.
–3
–2
–1
1
2
3
4
x
c.
?
, from above
d.
, from below
8. Below is the graph of
.
c. oblique asymptote
d. None
7. Let
what direction does
a.
, from above
____
?
. What are the critical number(s)?
c.
,
,
,
,
, and
d.
,
be a polynomial of degree 3 and
. Let
be a polynomial of degree 2 and
What type of asymptote is located at
____
?
and
and from
b.
____
9. Let
a.
b.
d.
. For what value(s) of
does
have a point of inflection?
c.
d. None
____ 10. Let
. Determine the concavity of
on the interval
.
a. Concave up
c. Neither concave up or concave down
b. Concave down
d. Unknown
____ 11. Which function has an oblique asymptote?
a.
c.
b.
d.
____ 12. Which of the following exponential functions is NOT always increasing on the entire real line?
a. f(x) =
c. f(x) =
b. f(x) =
d. f(x) =
____ 13. Determine the minimum value of the function
.
a. 0
c. 4
b.
d. There exists no minimum value.
____ 14. Which of the following x-coordinates is a candidate for being an extreme value for the function
?
a.
c. 1
b. 0
d. 2
____ 15. Determine the maximum value of the function
on the interval
.
a. 10.51
c.
b. 29.42
d.
____ 16. Which of the following is the minimum value of the function
?
a. 0
c.
b.
d. There does not exist a minimum value.
Application (A/15, C/10)
A. Find the linearization of the given function centered at
, and use it to estimate
. (A/5)
B. Given the sign chart below, complete and sketch the graph of the function f(x) (/A5)
x
-
x < -2
x = -2
-2 < x < -1
x = -1
-1 < x < 0
x=0
x>0

f ’(x)
-
-
-
-
0
+
+
+
+
f “(x)
-
-
0
+
+
+
+
+
+
f(x)
y=0
C. Determine the absolute extreme values of the function f(x) = 2 sin x – x
Thinking (T/15 C/10)
D. Let
. Determine the equations of all of the asymptotes of
on the interval
. (A/5)
. If the function has vertical asymptotes,
determine the behavior of the function left and right of the vertical asymptotes (/T5)
E. Below is the graph of
. For what values of
is
concave up? Justify your answer. (/T5)
f '( x)
–8
–7
–6
–5
–4
–3
–2
–1
1
2
3 x
F. Give an example of a function that has at least one vertical asymptote and an oblique asymptote. Justify your answer.
(/T5)