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
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
x
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





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.
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23.
y
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24.
y
x



B.

C.
y


26. y  x 3x 2  2



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
D.
y
x

y
x
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x
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x

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
y
25.
y
x
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
A.

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y
x

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
x
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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