# How do I find the absolute minimum and maximum of a function using its derivatives?

Mar 20, 2017

Derivating a function will give us its gradient for every $\left(x , y\right)$ on it. At the minima and maxima, the gradient of the function will be zero.
So once we've found the derivative, if we want to find the minima and maxima, we set the derivative equal to zero and solve for $x$. Once we've found the value of $x$, we should calculate $f ' ' \left(x\right)$, and this will tell us if the stationary point at $x$ is a minimum or maximum.
We can then use a table of values to see if $y$ is increasing or decreasing around the turning point and this will help identify if it's a local or absolute stationary point.