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Practice Test Function Analysis with CalculusName______________________________________________
1. Match each function graph with its derivative graph.
Functions:
Derivatives:
Given this graph of the derivative, g’(x), fill in the table for g(x).
Characteristic
g(x)
Intervals of increase
Intervals of decrease
Minima
Maxima
Point(s) of inflection
Concave up
Concave down
3. Use the given information to sketch the curve. Fill in the table for each problem.
a. The graph of f’(x)…
Characteristic
g(x)
Intervals of increase
Intervals of decrease
Minima
Maxima
Point(s) of inflection
Concave up
Concave down
b. This table
X
-3
1
4
f(x)
-3
3
5
f’(x)
Negative
0
Positive
Positive
0
negative
f”(x)
Positive
Positive
0
Negative
negative
Characteristic
g(x)
Intervals of increase
Intervals of decrease
Minima
Maxima
Point(s) of inflection
Concave up
Concave down
c. This function:
Characteristic
g(x)
Intervals of increase
Intervals of decrease
Minima
Maxima
Point(s) of inflection
Concave up
Concave down
4. Find the absolute maximum and absolute minimum of the function on the given interval.
a.
b.
5. These three graphs are a function, its first derivative and its second derivative. Figure out which one is which.
Fill in the blanks.
6. When the second derivative is negative the function is _________________________.
7. When the derivative is increasing, the second derivative is ___________________________.
8. When the derivative is negative the function is ____________________________.
9. When the function has a local maximum, the derivative changes from __________________ to _________________.
10. When the second derivative changes signs, the function has a _______________________________________.
11. The slope of the function is 0 when the derivative is _________________________.
12. An exponentially increasing function has a ___________________ that is always positive.
13. If the slope of a function is increasing, the second derivative is _______________________________.
14. If the function has a maximum, the second derivative is _________________________________.
15. If a function has a plateau, the derivative does not change _________________.
3
x
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fxx
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fxxx
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32
693[3,0]
yxxx
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