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I know that we should check critical numbers (points where f'(x) is either zero or not defined) and endpoints (for a closed interval) as possible points of local extrema of f(x). Obviously, all these points should be in the domain of f. So why does the following problem also test x = 0, which is not in the domain of f?

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  • $\begingroup$ How come do you claim they test $0$? $\endgroup$
    – Git Gud
    Nov 22, 2014 at 14:36

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In order for the testing to work, the function must be continuous on the entire test interval. This function is not continuous (or even defined) at $x=0$. As you can see, the function in fact changes direction as one moves from the left to the right of 0.

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  • $\begingroup$ So the solution is wrong? $\endgroup$
    – Leponzo
    Nov 22, 2014 at 15:29
  • $\begingroup$ @Leponzo No, it's correct. This is the reason the interval needs to be split at 0. $\endgroup$
    – Matt Samuel
    Nov 22, 2014 at 15:36

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