Functions

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 :