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6-40.

If f(x) is a continuous function, f ′(2) = −1, and f ′(3) = 1, does there have to be an x-value a such that 2 < a < 3 and f ′(a) = 0 ? Draw a sketch to support your explanation. Homework Help ✎

A function may be continuous without being differentiable at all points.