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Question

Let f(x)=x21x2 and g(x)=x1x,xR1,0,1. If h(x)=f(x)g(x) then the local minimum value of h(x) is:

A
22
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B
22
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C
2
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D
3
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Solution

The correct option is D 2
f(x)=x21x2,g(x)=x1x,xR(1,0,1)h(x)=f(x)g(x)

=(x21x2)(x1x)

=(x1x)(x+1x)(x1x)

=(x+1x)h(x)=(x+1x)

Now, we know, Arithmetic Mean Geometric Mean

(x+1x)2x1x1 x+1x2

The min. value of h(x)=2

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