Chapter 10.1, Problem 17E

For each function in Problems 15-20

(a) find $y\text{'}=f\text{'}\left(x\right).$

(b) find the critical values.

(c) find the critical points.

(d) find intervals of x-values where the function is increasing and where it is decreasing.

(c) classify the critical points as relative maxima, relative minima, or horizontal points of inflection. In each case, check your conclusions with a graphing calculator.

$y=\frac{x^3}{3}+\frac{x^2}{2}-2x+1$