Chapter 10:
Graphing and Optimization
Review for Test #2
1.
Pages 703 (11 – 38) and Page 705 (51 – 72)
Use the first derivative test to determine intervals where the function is increasing and decreasing.
Find all
local extrema.
Example:
f(x) = 2x
3
– 3x
2
– 12x – 5
2.
Page 642 (43 – 48)
Find the second derivative for y = (x
2
– 16)
5
3.
Page 723 (23 – 60)
Find the intervals where f(x) is concave up and concave down.
Find all inflection points.
Example:
f(x) = x
3
– 18x
2
+ 10x – 11
4.
Page 725 (43 – 46)
Find the point of diminishing returns (when the rate of change is optimum).
Example:
A company estimates that it will sell N(x) units of a product after spending x thousands of
dollars
on advertising as given by
N(x) =

0.25x
4
+ 13x
3
– 180x
2
+ 10,000 where 15 <
x
<
45.
What is the point of diminishing returns (when the rate of change is a maximum)?
5.
Page 738 (11 – 28)
Find all horizontal asymptotes, vertical asymptotes, and holes, if any, for the graph of
a.
6
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 Calculus, Derivative, Mathematical analysis, Convex function

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