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 $$c \neq b$$

B

$$a = c$$ and $$a \neq b$$

C

$$a \neq b$$ and $$c \neq b$$

D

$$a = b = c$$