Question: Show there does not exist a continuously differentiable function f on [0, 2] such that f(0) = -1, f(2) = 4, and f(x) < 2

Show there does not exist a continuously differentiable function f on [0, 2] such that f(0) = -1, f(2) = 4, and fʹ(x) < 2 for 0 < x < 2. (Apply the Fundamental Theorem.)

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