Problem 49E

49. (a) Graph the function

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

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 $f^{\prime}$. (See Example 2.2.1.)

(c) Calculate $f^{\prime}(x)$ and use this expression, with a graphing device, to graph $f^{\prime}$. Compare with your sketch in part (b).

Step-by-Step Solution