### Home > CALC > Chapter 5 > Lesson 5.2.3 > Problem5-86

5-86.

Algebraically determine where $g(x)$ below is increasing, decreasing, concave up, and concave down.

$g(x) = x^3 − 2x^2 + x − 1$

The function $f(x)$ is increasing when $f^\prime(x) > 0$, and it is decreasing when $f^\prime(x) < 0$.
The function is concave up when $f^{\prime\prime}(x) > 0$, and it is concave down when $f^{\prime\prime}(x) < 0$.