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Question

The greatest value of f(x)=(x+1)1/3(x1)1/3on[0,1] is

A
1
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B
2
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C
3
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D
1/3
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Solution

The correct option is C 1
f(x)=(x+1)1/3(x1)1/3differentiatew.r.t.xf(x)=13(x+1)2/313(x1)2/3f(x)13[(x+1)2/3(x1)2/3]=0(x+1)2/3=(x1)2/3(x1)2/3=(x+1)2/3x=0f′′(x)=13[23(x+1)5/3+23(x1)5/3]putx=0f(0)=(0+1)1/3(01)1/3=1(1)1/3Greatestvaluesis1

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