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Question

If f(x)=(x1)2(x+1)2, then the function f has

A
a local maximum at x=15
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B
a local minimum at x=15
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C
a local minimum at x=1
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D
a local maximum at x=1
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Solution

The correct option is A a local maximum at x=15
f(x)=(x1)2(x+1)3
f(x)=2(x1)(x+1)3+3(x+1)2(x1)2=0(x1)(x+1)2(5x1)=0x=1,15,1
f(x) has local maxima at 15

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