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2. Suppose that f, g, h are three functions defined on (a, b) and c (a, b). Assume that f and h are differentiable at c, f(c) = h(c), and f(x) g(x) h(x) for all x (a, b).
Prove that g is also differentiable at c and (c) = (c) = (c).
Differentiability of a function is investigated in the solution.