CPM Homework Help : APCALC Problem 5-86

Algebraically determine where the function $g$ given below is increasing, decreasing, concave up, and concave down.

$g\left(x\right) = x^{3} – 2x^{2} + x – 1$

Hint:

The function $f\left(x\right)$ is increasing when $f'(x)>0$ , and it is decreasing when $f'(x)<0$ .
The function is concave up when $f''(x)>0$ , and it is concave down when $f''(x)<0$ .