Chapter 3 - The Derivative In Graphing And Applications - 3.2 Analysis Of Functions II: Relative Extrema; Graphing Polynomials - Exercises Set 3.2 - Page 205: 8

See the explanations.

\[ \begin{aligned} &12 x +3 x^{4}=f(x) \\ &12+12 x^{3}= f^{\prime}(x) \\ &=12\left(1+x^{3}\right) \\ &=12(1+x)\left(-x+1+x^{2}\right) \end{aligned} \] $x=-1$ is the critical point. $x=-1$ is a stationary point also, as the given function is differentiable.