Chapter 4, Problem 1RE

a.

To determine

The intervals on which the function $f\left(x\right)=\frac{1}{3}{x}^3-x^2+x-6$ is increasing and decreasing.

b.

To determine

The relative extrema of the function $f\left(x\right)=\frac{1}{3}{x}^3-x^2+x-6$.

c.

To determine

The intervals on which the graph of the function $f\left(x\right)=\frac{1}{3}{x}^3-x^2+x-6$ concave upward and concave downward.

d.

To determine

The inflection point of the function $f\left(x\right)=\frac{1}{3}{x}^3-x^2+x-6$.