# How do you find the coordinates of the local extrema of the function?

##### 1 Answer

The best way to do this is to find the derivative of the function.

Let's say our function is

First, we take the derivative of the function. Remember:

So:

Now we need to find the point where

So

The last step is to plug this x value into the *original* equation.

So the local minimum is at

Note that I deliberately didn't pick a "nice and easy" function - this is to show that finding the derivative, and making the derivative equal zero, works for everything.