Math 170010
Homework 9/2
Fall 2011
Goals:
•
Compute
f
′
at many locations.
•
Interpret this data as a function and be able to graph it.
Exercises:
1. From the Online Textbook, Section 2.4: Problems 6 and 7. As the author instructs.
Note
that these instructions mean that your solution must include a table of
x
and
f
′
values that
includes at least:
•
Locations where
f
′
= 0.
•
Locations where
f
′
fails to exist (corners or jumps).
•
At least some other locations.
•
Slope data for all these locations.
From this table you should sketch a graph of
f
′
. Your graph of
f
′
must clearly indicate what
is happening near any place where
f
′
does not exist.
2. Turn to page 42 of the Online Textbook.
For each of the graphs labeled (b), (c) and (d),
estimate the derivative at a number of points, including any “special” points. Then graph the
derivative.
3. Graph the function
f
(
x
) = cos
x
on the domain,

2
π
≤
x
≤
2
π
. Use your graph to estimate
the derivative at a number of points, including any “special” points. Then graph the derivative.
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 Fall '08
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 Math, Calculus, Approximation, Derivative, 1.5 ft, online textbook

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