What is the name of the point where the slope of a function changes suddenly?

I am looking for the name of the point where the function changes its slope suddenly. So at this point:





y'=f'(k+) = +ve and


y'=f'(k)=0 and


y'=f'(k-) = -ve





Here I am taking the derivative of a function f(x) at the point k where the graph or plot of the function looks like a kink. I am betting that this will still be inflection point but I wanted the opinion of the experts out there. :)





Thanks!

What is the name of the point where the slope of a function changes suddenly?
[Answer: I would think you meant a critical point? Inflection point determines more of a change in concavity, while a critical point determines whether a point is a maxima or minima (thus, a change in of slope).]
Reply:You're thinking of a discontinuity





All you described was a normal max or mix, the slope at the point of a discontinuity is undefined and has no derivative as a result
Reply:would that be "local maxima" or "local minima"
Reply:Maximum turning point, minimum turning point. Point of inflection, too.
Reply:critical point

karate