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Example 6

Find the maximum of f(x) = 1 - x2/3.

Step 1

f'(x) = -(⅔)x-1/3.

Step 2

f'(x) is undefined at x = 0, and this the only critical point.

Step 3

We use the Direct Test. Let

u = -1, v = 1. f(0)=l, f(-l) = 0, f(l) = 0.

Thus f has a maximum at x = 0, as shown in Figure 3.5.11.

If f has more than one interior critical point, the maxima and minima can sometimes be found by dividing the interval into two or more parts.

03_continuous_functions-161b.gif

Figure 3.5.11
Home Continuous Functions Maxima and Minima Examples Example 6

Last Update: 2006-11-25