Question: Suppose that a function f(x) defined for all x has a continuous derivative f' (x) defined for all x and suppose that f is decreasing

Suppose that a function f(x) defined for all x has a continuous derivative f' (x) defined for all x and suppose that f is decreasing for x < 1 and f is increasing for x > 1. Is it true that there exists a point x₀ between 1 and 1 such that f'(x₀) = 0?

T or F?

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