# Calc2.52

From Example Problems

Find the local minimums and maximums of the function .

To find the local minimums and maximums of a function, find the critical points by finding the derivative and finding the points where it is equal to 0 or undefined. If the original function is defined at these points, then these are critical points.

This function is never equal to 0 as the numerator is never equal to 0. It is undefined at . This is our only critical point. However, the square root function is only defined for nonnegative real numbers so is not defined to the left of . Thus, it can not have a local minimum or maximum at . does give us the lowest point on the entire square root function as it starts at and increases thereafter.