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Let f,g and h be real-valued functions d...

Let f,g and h be real-valued functions defined on the interval [0,1] by `f(x)=e^(x^(2))+e^(-x^(2)),g(x)=xe^(x^(2))+e^(-x^(2))` and `h(x)=x^(2)e^(x^(2))+e^(-x^(2))` , If a, b and c denote respectively the absolute maximum of f,g and h on [0,1], then

A

a=b and `c ne b`

B

a=c and `a ne b`

C

`a ne b and c ne b`

D

a=b =c

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The correct Answer is:
D
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