differentiable function

Let f and g be two non- decreasing twice differentiable function defined on an interval (a,b) such that for each x $\in$ ( a, b) , f”(x) = g(x) and g”(x) = f(x) . Suppose also that g(x)f(x) is linear in x on ( a ,b) . Show that we must have f(x) = g(x) = 0 for all x$\in$ (a , b).

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