<P> A turning point is a point at which the derivative changes sign . A turning point may be either a relative maximum or a relative minimum (also known as local minimum and maximum). If the function is differentiable, then a turning point is a stationary point; however not all stationary points are turning points . If the function is twice differentiable, the stationary points that are not turning points are horizontal inflection points . For example, the function x ↦ x 3 (\ displaystyle x \ mapsto x ^ (3)) has a stationary point at x = 0, which is also an inflection point, but is not a turning point . </P> <P> Isolated stationary points of a C 1 (\ displaystyle C ^ (1)) real valued function f: R → R (\ displaystyle f \ colon \ mathbb (R) \ to \ mathbb (R)) are classified into four kinds, by the first derivative test: </P> <Ul> <Li> a local minimum (minimal turning point or relative minimum) is one where the derivative of the function changes from negative to positive; </Li> <Li> a local maximum (maximal turning point or relative maximum) is one where the derivative of the function changes from positive to negative; </Li> </Ul> <Li> a local minimum (minimal turning point or relative minimum) is one where the derivative of the function changes from negative to positive; </Li>

When does a function have no stationary points