If there is a
function f on an interval
I which contains the point
c, c is a critical point if at least one of the following is true:
1. c is an end point on the interval I.
2. c is a stationary point(Where the slope of the tangent(derivative) is equal to 0).
3. c is a singular point(Where the derivative does not exist).
Critical points can help you find out where the function is increasing and/or decreasing which in turn can help you find minima and maxima.