(a) Graph the function

$ f(x) = x^4 - 3x^3 - 6x^2 + 7x + 30 $

in the viewing rectangle [-3,5] by [-10,50].

(b) Using the graph in part (a) to estimate slopes, make a rough sketch, by hand, of the graph of $ f' $.

(c) Calculate $ f'(x) $ and use this expression, with graphing device, to graph $ f' $. Compare with your sketch in part (b).