Chapter 3: Answers 1 Jack K. Cohen Colorado School of Mines
x |
[- 1, - ![]() |
(- ![]() ![]() |
(![]() |
f' | - | + | - |
f | ![]() |
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The arrows in the table indicate whether f is increasing/decreasing (we get the third row from the second of course). We see that the candidates for maximum are x = - 1 and
x = , evaluating f at these points shows that the maximum is at
x =
. Similarly
x = -
gives the minimum. See Figure 3.
Since we know that the derivative is 2x, and the graph is apparently a straight line through the points (0, 0) and (1, 2), the approximate slope function seems to be a fine approximation to the derivative—at least on the crude graphics level.