QuestionAnalyze the graph of $f^{\prime}$, then list all inflection points and intervals where $f$ is concave up and concave down. (Enter your answer for inflection points as a comma-separated list. Enter your answers for concavity using interval notation. If an answer does not exist, enter DNE.) locations of inflection points $\quad x=$ $\square$ concave up $\square$ concave down $\square$

Studdy Solution
List the inflection points and concavity intervals based on the analysis.
Inflection points occur at $x = -1$ and $x = 3$ where $f'(x)$ changes sign.
Concave up intervals for $f$ occur where $f'(x)$ is increasing: $(-2, 0) \cup (2, \infty)$.
Concave down intervals for $f$ occur where $f'(x)$ is decreasing: $(0, 2)$.
The solution is:
Locations of inflection points $x = -1, 3$
Concave up $(-2, 0) \cup (2, \infty)$
Concave down $(0, 2)$