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Let f, g, h be real valued functions def...

Let f, g, 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, c respectively denote the absolute maximum of f, g and h on [0, 1] then show that a =b=c.

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