Critical point of a piecewise function

[mohammed El-Kady]

TL;DR Summary

critical point to piece wise function

If the function is not differentiable at point. Can we consider this point is critical point to the function?
f(x) = (x-3)^2 when x>0
= (x+3)^2 when x<0
he asked for critical points in the closed interval -2, 2

 

[member 587159]

Please define critical point.

 

[mohammed El-Kady]

Please define critical point.

you don't know it?

 

[mathman]

" When dealing with functions of a real variable, a critical point is a point in the domain of the function where the function is either not differentiable or the derivative is equal to zero." definition from Wikipedia Looks like the answer is yes. (derivative discontinuous)

 

[member 587159]

you don't know it?

Different people use different definitions... The answer to your question depends on the definition you are using.

 

[mohammed El-Kady]

" When dealing with functions of a real variable, a critical point is a point in the domain of the function where the function is either not differentiable or the derivative is equal to zero." definition from Wikipedia Looks like the answer is yes. (derivative discontinuous)

thank you

 

[mohammed El-Kady]

Different people use different definitions... The answer to your question depends on the definition you are using.

I don't know which definition the problem ask for. I know the definition of the derivative, but someone solved it with the differentiability , so i need to be sure from it.

 

[DaveE]

critical point vis-a-vis finding minima/maxima? Yes, you have to evaluate those points. Think of a "V" shaped function. How else would you find the minimum.

 

[FactChecker]

I don't think you meant to do this, but you have not defined the function at x=0, so it is not a critical point of the function.