Stationary Points


a function is said to be increasing when its gradient is positive and decreasing when the gradient is negative. 

a stationary point occurs on the curve of a function when the gradient at that point is zero. stationary points can be minimum points, maximum points or points of inflection.

a point of inflection does not have to be a stationary point

Key Skills

  • inspect the curve of a function and state where the function is increasing or decreasing and identify any stationary points or points of inflection
  • find the coordinates and nature of turning points and points of inflection by examining the gradient either side of the point or using the second derivative test.


functiongradient, increasing function, decreasing functionturning pointstationary pointpoint of inflectionminimum point, maximum point