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Home Continuous Functions Maxima and Minima Examples Example 8
 
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Example 8

f(x) = x3 - 1.

Test for maxima and minima.

Step 1

f'(x) = 3x2.

Step 2

f'(x) = 0 only when x = 0.

Step 3

The Second Derivative Test fails, because f"(x) = 6x, f"(0) = 0. By direct computation, f(0) = -1, f(-1) = -2, f(1) = 0. Therefore f has neither a minimum nor a maximum at x = 0.

CONCLUSION

Since x = 0 is the only critical point of f and f doesn't have a maximum or minimum there, we conclude that f has no maximum and no minimum as shown in Figure 3.5.13.

03_continuous_functions-164.gif

Figure 3.5.13
Home Continuous Functions Maxima and Minima Examples Example 8

Last Update: 2006-11-25