Points on the graph of a function at which the derivative is zero or does not exist at all are called critical points i.e. The point (x, f (x) ) is a critical point of f (x) , if x is in the domain of 'f'' and either f ' (x) = 0 or DNE. Geometrically speaking, the tangent at such a point to the curve representing the function y = f (x) is either horizontal, vertical or DNE.

5.1 Tangent And Normal Lines
5.2 Angle Between Two Curves
5.3 Interpretation Of The Sign Of The Derivative
5.4 Locality Increasing Or Decreasing Functions
5.5 Critical Points
5.6 Turning Points
5.7 Extreme Value Theorem
5.8 The Mean-value Theorem
5.9 First Derivative Test For Local Extrema
5.10 Second Derivative Test For Local Extrema
5.11 Stationary Points
5.12 Concavity And Points Of Inflection
5.13 Rate Measure (distance, Velocity And Acceleration)
5.14 Related Rates
5.15 Differentials : Errors And Approximation