Problem

Problem

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) = x e^{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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