Where defined in math

Turning point - turning point and turning points

There is also such a point with many functions. This point is where the slope of the function (the slope of a function is determined by the derivative function) is strongest. Because before the slope is getting stronger and afterwards weaker again due to the opposite curvature.

Consequently, where the derivative function is most extreme (i.e. where it has an extreme point), there is a turning point. The extreme values ​​for a function were calculated by its derivative, that of the derivative by the second derivative of the function, with the necessary condition that it becomes zero.

The following conditions must therefore be met:

If f '' '(x)> 0, then x is a right-left turning point and if f' '' (x) <0, then x is a left-right turning point.

We calculate an example. Our function is given by:

We need the first derivative to form the second:

We form the second derivative:

We set the second derivative equal to zero:

Our turning point is at x = 1. We plug this x value into our function to get the y value:

Our turning point is therefore W (1 | 0). Quickly check the third derivative that it does not become zero either: