# How do you find the extreme values of the function and where they occur?

To find extreme values of a function $f$, set $f ' \left(x\right) = 0$ and solve. This gives you the x-coordinates of the extreme values/ local maxs and mins.
For example. consider $f \left(x\right) = {x}^{2} - 6 x + 5$. To find the minimum value of $f$ (we know it's minimum because the parabola opens upward), we set $f ' \left(x\right) = 2 x - 6 = 0$ Solving, we get $x = 3$ is the location of the minimum. To find the y-coordinate, we find $f \left(3\right) = - 4$. Therefore, the extreme minimum of $f$ occurs at the point $\left(3 , - 4\right)$.