Does a Non-Injective Differentiable Function Have a Zero Derivative Point?

2RIP · Nov 10, 2007

If an interval is differentiable, but not injective, will there be a point where the derivative f'(x)=0 on that interval?

I'm not really sure how to approach this question. Help please?

HallsofIvy · Nov 10, 2007

Use the mean value theorem. f f(x) is not injective, then there must exist x1 and x2 such that f(x1)= f(x2). Apply the mean value theorem to the interval [x1, x2].

Does a Non-Injective Differentiable Function Have a Zero Derivative Point?

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Does a Non-Injective Differentiable Function Have a Zero Derivative Point?

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