Question

score on last try: 0 of 10 pts. see details for more. at least one scored part is incorrect. jump to first changeable incorrect > next question get a similar question you can retry this the function graphed above is: concave up on the interval(s) concave down on the interval(s) there is an inflection point at: question help: video enter a point more... submit question

Explanation:

Step1: Recall concavity definitions

A function is concave - up when the second - derivative is positive and concave - down when the second - derivative is negative. Inflection points occur where the concavity changes.

Step2: Observe the graph

Visually, a function is concave up when it looks like a "cup" and concave down when it looks like a "cap".
Looking at the graph, the function is concave up on the interval $(-1,3)$.
The function is concave down on the intervals $(-\infty,-1)\cup(3,\infty)$.
The inflection points occur where the concavity changes, which are at $x = - 1$ and $x = 3$. In point form, the inflection points are $(-1,f(-1))$ and $(3,f(3))$. Since we are just asked for the $x$ - values, the inflection points are at $x=-1$ and $x = 3$.

Answer:

Concave up on the interval(s): $(-1,3)$
Concave down on the interval(s): $(-\infty,-1)\cup(3,\infty)$
There is an inflection point at: $x=-1,x = 3$