Question

question 3 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 submit question

Explanation:

Step1: Recall concavity rules

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

Step2: Observe the graph

Visually, the function is concave up on the intervals where the curve "holds water". Looking at the graph, the function is concave up on the intervals \([-1,3]\).

Step3: Find concave - down intervals

The function is concave down on the intervals where the curve "spills water". The function is concave down on the intervals \((-\infty,-1)\cup(3,\infty)\).

Step4: Locate inflection points

Inflection points are where the concavity changes. From the graph, the inflection points occur 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: \(x=-1,x = 3\)