Consider the following function.

y=x^3/3 + x^2/2 2x+7

(a) Findy'=f'(x).

f'(x) =

(b) Find the critical values. (Enter your answers as a comma-separated list.)

x=

(c) Find the critical points.

(x,y)=(smallerx-value)(x,y)=(largerx-value)

(d) Find intervals ofx-values where the function is increasing. (Enter your answer using interval notation.)

Find intervals ofx-values where the function is decreasing. (Enter your answer using interval notation.)

(e) Classify the critical points as relative maxima, relative minima, or horizontal points of inflection. In each case, check your conclusions with a graphing utility. (If an answer does not exist, enter DNE.)

relative maxima(x,y)

=

relative minima(x,y)

=

horizontal points of inflection(x,y)