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Home Continuous Functions Maxima and Minima Examples Example 5
 
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Example 5

Find the minimum of

f(x) = x6 + 10x4 + 2.

Step 1

f'(x) = 6x5 + 40x3 = x3(6x2 + 40).

Step 2

f'(x) = 0

only when

x = 0.

Step 3

The Second Derivative Test fails, because

f"(x) = 30x4 + 120x2, f"(0) = 0.

We use the Direct Test. Let

u = -1, v = 1.

Then

f(0) = 2, f(-1) =13, f(1) = 13.

Hence f has a minimum at 0, as shown in Figure 3.5.10.

03_continuous_functions-161a.gif

Figure 3.5.10
Home Continuous Functions Maxima and Minima Examples Example 5

Last Update: 2006-11-25