Use the Mean Value Theorem to show the following assertions (a) Suppose that f(x) is continuous on [0, 4] and differentiable on (0, 4). If f(4) < f(0) show that f'(c) < 0 for some c between 0 and 4. (b) Suppose that g(x) is a differentiable function. Show that if g'(x) ≤ 5 for all x, then g(12) ≤ 10 + g(10).

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A: Topic:- Functions

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A: We want to prove the given result.

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