# When finding the maximum and minimum points of a function on an interval what do you do if the derivative is undefined at zero

Say I have a function and I want to find the maximum and minimum on an interval, I would first differentiate the function and equate it to zero. Then use this value and the two ends of the interval to find the max and min. If, however the the derivative is undefined when it equals zero do I just scrap that as a value and use the bounds of the interval in the original function? does this mean that when its equal to zero its a critical point?

How can it equal zero and be undefined? In any case, points where the derivative is undefined are candidates for the max/min (in addition to the endpoints of the interval and points where the derivative is zero), so you should check the value of $f$ at those points too.
• I see what you mean. Then there are no points $x$ such that $f'(x)=0$, so the only candidates for the max/min will be points $x$ such that $f'(x)$ is undefined, and the endpoints of the interval. – kccu Dec 12 '17 at 18:44