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A differentiable function f satisfies 1 f x 3 for all

A differentiable function f satisfies 1 ≤ f ′(x) ≤ 3 for all real numbers x .

Moreover, it is known that f (2) = 4 . Use the Mean Value Theorem to answer the following.

(a) What is the largest possible value of f(7) ? Explain.

(b) What is the smallest possible value of f(-4) ? Explain.

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Mathematics: A differentiable function f satisfies 1 f x 3 for all

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