Ma 113 Functions And Inverse Functions, The Exponential Function And The Logarithm Worksheet Page 25
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41Worksheet # 19: The Shape of a Graph
1. Explain how to use the second derivative test to identify and classify local extrema of a twice differen-
tiable function ( ). Does the test always work? What should you do if it fails?
2. Suppose that ( ) is differentiable for all
and that
5
( )
3 for all . Assume also that
(0) = 4. Based on this information, use the Mean Value Theorem to determine the largest and
smallest possible values for (2).
3. A trucker handed in a ticket at a toll booth showing that in 2 hours she had covered 159 miles on a toll
road with speed limit 65 mph. The trucker was cited for speeding. Why did she deserve the ticket?
4. (a) Consider the function ( ) =
8
+ 5.
i. Find the intervals on which the graph of ( ) is increasing or decreasing.
ii. Find the intervals of concavity of ( ).
iii. Find the points of inflection of ( ).
3
(b) Repeat with the function ( ) = 2 + sin( ) on
.
2
2
4
(c) Repeat with the function ( ) =
+
.
(d) Repeat with the function ( ) =
.
5. Below are the graphs of two functions.
(a) Find the intervals where each function is increasing and decreasing respectively.
(b) Find the intervals of concavity for each function.
(c) For each function, identify all local extrema and inflection points on the interval (0,6).
6. Find the local extrema of the following functions using the second derivative test:
(a)
( ) =
5 + 4
(b) ( ) = 5
10 ln(2 )
7. Find the local extrema of ( ) = 3
5
+ 10 using the second derivative test where possible.
8. Sketch a graph of a continuous function ( ) with the following properties:
is increasing on (
3)
(1 7)
(7
)
is decreasing on ( 3 1)
is concave up on (0 3)
(7
)
is concave down on (
0)
(3 7)
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education