Question

score on last try: 0 of 1 pts. see details for more.
at least one scored part is incorrect. jump to first changable incorrect part.

next question you can retry this question below

the function graphed above is:
concave up on the interval(s)
concave down on the interval(s)
there is an inflection point at:

Explanation:

Step1: Recall the definition of concavity

A function \(y = f(x)\) is concave up when \(f''(x)>0\) and concave down when \(f''(x)<0\). An inflection point is a point where the concavity changes, i.e., \(f''(x) = 0\) and the sign of \(f''(x)\) changes around that point.

Step2: Analyze the graph

Looking at the graph, we can see that the function is concave up on the interval \((-\infty, 1.6)\) and concave down on the interval \((1.6,4.2)\). The inflection point is at \(x = 1.6\) (where the concavity changes from up - to - down).

Answer:

Concave up on the interval(s): \((-\infty,1.6)\)
Concave down on the interval(s): \((1.6,4.2)\)
There is an inflection point at: \(1.6\)