Find the critical values of a cubic:

The extrema or critical values are located where the derivative of f(x) is zero. We can use the Power, Scalar Multiple, and Sum Rules to get

Setting this to 0 and factoring, we get

Since f ' is defined for all values of x, the critical numbers are -3 and +2.

Next we wish to use the First Derivative Test to determine the slope of the graph of f(x) in the 3 intervals defined by these two values as shown in the following table:

Next determine the algebraic sign of the first derivative at each of these points.