- #1

MidgetDwarf

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- 671

I recalled the theorem by memory.

Let the function f be defined on the closed interval from a to b and have a relative maximum or minimum at x=c, where c is in the open interval from a to b.

If the derivative exist as a finite number at x=c, then the derivative is o at that point.

I went through the derivation of the proof, and the theorem (by analyzing my derivation), does not say what happens when.

1) when the derivative fails to exist at a point c.

2) at the endpoints, or that there is always a max or min when the derivative equals 0.

I sometimes tutor my little neighbor next door for free, because it helps me practice things I havnt used in a while. Today I told him, that a relative max or min can occur if the function is defined at that point, does not have to be necessary differential at that point. I use y=|x| as an example.

I felt bad, because I believed I gave him the wrong answer. Sorry for the long post.