Does every point of minimum local has derivative equal to zero?

Asked Apr 28 '21 at 14:53

Active Apr 28 '21 at 14:53

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I have to answer if it's true or false that every minimum point of a function happens where the derivative is null.

But I was wondering about $f(x)=|x|$ which clearly has global (local) minimum at $x=0$, but we're not able to calculate $f'(0)$.

So, is the affirmative false?

asked Apr 28 '21 at 14:53

mvfs314

local minimum, not minimum local. – Apr 28 '21 at 15:00
2

If the derivative exists, it must be zero (not counting the endpoints of the domain). – Apr 28 '21 at 15:02
First you need the proposition to be completely clear, before you want to see if it is true or not. – Asinomás Apr 28 '21 at 15:12
@HereToRelax the proposition is exactly that: very minimum point of a function happens where the derivative is null. – mvfs314 Apr 28 '21 at 15:20
Sure, but what kind of function? – Asinomás Apr 28 '21 at 15:31
@HereToRelax the proposition is exactly that. No more info. – mvfs314 Apr 28 '21 at 15:33
Oh, you mean in your homework? – Asinomás Apr 28 '21 at 15:38
@HereToRelax yes – mvfs314 Apr 28 '21 at 16:54

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