Definitions:

1. A number a in the domain of a given function f is called a critical number of f if f '(a) = 0 or f ' is undefined at x = a.

2. Relative extrema are the minimums or maximum points on a part of a curve, while absolute extrema are the minimums and maximum points along the entire curve.

Now we are looking at the following curve:

f (x) =

To find the extrema, we take the first derivative and figure out at what value of x, the first derivate of the function equals to zero:

f’(x) = 2x-6

f’(3) = 0

As you can see the function is decreasing from negative infinity to 3, and increasing from 3 to infinity. The critical number is 3. There is only one relative (or local) minimum at (3, -9).