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Question

The function f(x)=x2(x2)2


A

Decreases on (0, 1) (2, )

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B

Increase on (, 0) (1, 2)

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C

Has a local maximum value 0

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D

Has local maximum value 1

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Solution

The correct option is D

Has local maximum value 1


f(x)=x2(x2)2


f(x)=2x(x2)2+2x2+(x2)=4x(x2)(x1)

f(x)0 for x ε[0,1][2,]f(x)0 for x ε(,0)[1,2]


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