Textbook Problem

In Problems 29 and 30, complete the following for each function.

(a) Find f'(x).

(b) Check your result in part (a) by graphing both it and the numerical derivative of the function.

(c) Find x-values for which the slope of the tangent is 0.

(d) Find points (x, y) where the slope of the tangent is 0.

(e) Use a graphing utility to graph the function and locate the points found in part (d).

$f\left(x\right)={\left(x^2-4\right)}^3+12$