Math Wiki

In calculus, a stationary point is a point at which the slope of a function is zero. Stationary points can be found by taking the derivative and setting it to equal zero. For example, to find the stationary points of

one would take the derivative:

and set this to equal zero.

This gives the x-value of the stationary point. To find the point on the function, simply substitute this value for x in the original function.

So the coordinates for the stationary point would be .

One can then use this to find if it is a minimum point, maximum point or point of inflection.

This can be done by further differentiating the derivative and then substituting the x-value in. If the calculation results in a value less than 0, it is a maximum point. If the calculation results in a value greater than 0, it is a minimum point. If the calculation is equal to 0, it is a point of inflection.