First Derivative Test For Relative Extrema

Since $$p'(x)=3*(x-1)*(x-3)$$, the function has a relative maximum at $$x=1$$ (where the derivative changes from positive to negative) and a relative minimum at $$x=3$$ (where it changes from negative to positive).

The function has a relative maximum at $$x=3$$ and a relative minimum at $$x=1$$ because the derivative is zero at both points.

Relative extrema cannot be determined using the first derivative test because the derivative does not change sign at the critical points.

The function possesses no relative extrema since the first derivative test applies only to functions with quadratic behavior.