If a critical point is equal to zero, it is called a stationary point (where the slope of the original graph is zero). If it does not exist, this can correspond to a discontinuity in the original graph or a vertical slope.
A critical point equal to zero may indicate the presence of an extreme value, if the second derivative of the function is non-zero. A positive second derivative indicates a local minima, and a negative second derivative indicates a local maxima. Note that some functions (e.g. or ) have critical points that aren't extreme values.