Question

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

Answer 1

See below.

Explanation:

To find extreme values of a function `f`, set `f'(x)=0` and solve. This gives you the x-coordinates of the extreme values/ local maxs and mins.

For example. consider `f(x)=x^2-6x+5`. To find the minimum value of `f` (we know it's minimum because the parabola opens upward), we set `f'(x)=2x-6=0` Solving, we get `x=3` is the location of the minimum. To find the y-coordinate, we find `f(3)=-4`. Therefore, the extreme minimum of `f` occurs at the point `(3,-4)`.