Question: Sketch the graph of a (simple) non constant function f that has a local maximum at x = 1, with f'(1) = 0, where f'

Sketch the graph of a (simple) non constant function f that has a local maximum at x = 1, with f'(1) = 0, where f' does not change sign from positive to negative as x increases through 1. Why can’t the First Derivative Test be used to classify the critical point at x = 1 as a local maximum? How could the test be rephrased to account for such a critical point?

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