Calculus BC
Section ____________
Name ______________________
Date _______________________
Assignment 3-E
Sketch a graph of the derivative of the function whose graph is shown.
1.
2.
3.
4.
y
y
y
y
x
x
x
x
Use the graph of f ′ shown and the given starting point to graph f (the antiderivative).
y
5.
6.
7.
y
y
8.
y
x
x
x
x
starting point 1, 2
starting point (0,0)
starting point (1,2)
starting point (0,0)
Use the graph of f ′ shown to sketch a graph of f ′′ and a possible graph of f .
9.
y
10.
y
11.
y
x
x
x
12. Find the vertical asymptotes, end behavior, and relative extrema. Then graph
1
f x 2
without using a calculator.
x 2x 8
13. If f x x x 4 , find relative extrema and points of inflection. Then graph f without
3
using a calculator. Hint: f x 12 x 4 x 2 .
14. Use the Second Derivative Test to find the relative extrema of f x x3 3x2 5.
15. Use the following information to sketch a possible graph of f .
f 0 f 4 0, f 2 2,
f x 0 when x 2, f x 0 when x 2, f 2 does not exist,
f x 0 when x 2
16. Find the c-value guaranteed by the Mean Value Theorem for f x x3 2x 3 on the
interval 0, 2.
17. Find the absolute minimum and absolute maximum of the function f x x3 12 x 2 on the
interval 0, 4 without using a calculator.
18. Without using a calculator, sketch a graph of f x x 2 6 x .
19. The graph of y ax 2 bx c passes through the point 1,6 and has a tangent line at
0,16
which is parallel to the graph of y 12 x 2 . Find a, b, and c.
20. If the only critical number of a function f (x) is x 3 , f 2 6, and f 4 7, does f
have a local minimum or a local maximum at x 3 ? Assume f is continuous.
21. If x 3 is a critical number of a function g (x) and g 3 6 , does g have a relative
minimum or a relative maximum at x 3 ?
Match the graph of f in the top row with the appropriate graph of f ′ in the bottom row.
22.
23.
y
24.
y
x
B.
C.
y
26. y x 3x 2 2
D.
y
x
y
x
x
x
y
25.
y
x
A.
y
x
x
27. x 2 2 xy y 8
28. Without using a calculator, find the domain, vertical asymptote, hole, x-intercept, and end
2 x2 2 x
f
x
.
behavior, and then graph
x2 x
0
