Question 20

Let $$f: R \rightarrow R$$ be an even function that is differentiable every where except exactly at 10 distinct points. Then which of the following statements is TRUE?

Solution

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An even function is symmetric about the y axis. Hence if there are 10 non-differential points, 5 of them lie towards the left side of the y-axis and 5 towards the right. Origin cannot be a non-differential point for an even function.

Hence $$f'\left(0\right)=0$$

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