on what open intervals is f concave up? select the correct choice and, if necessary, fill in the swer box to…

on what open intervals is f concave up? select the correct choice and, if necessary, fill in the swer box to complete your choice.\na. the graph of f is concave up on the open interval(s) (type your answer in interval notation. round to the nearest integer as needed. use a comma to separate answers as needed. )\nb. the graph of f is not concave up on any open interval.

on what open intervals is f concave up? select the correct choice and, if necessary, fill in the swer box to complete your choice.\na. the graph of f is concave up on the open interval(s) (type your answer in interval notation. round to the nearest integer as needed. use a comma to separate answers as needed. )\nb. the graph of f is not concave up on any open interval.

Answer

Explanation:

Step1: Recall the concavity rule

If (y = f(x)) is a differentiable function, then (f(x)) is concave up when (f^{\prime\prime}(x)>0). Also, by the relationship between the first - derivative and the second - derivative, if (f^{\prime}(x)) is increasing, then (f^{\prime\prime}(x)>0).

Step2: Analyze the graph of (y = f^{\prime}(x))

We look for the intervals where the graph of (y = f^{\prime}(x)) is increasing. From the graph of (y = f^{\prime}(x)), we can observe that the function (y = f^{\prime}(x)) is increasing on the intervals ((-20,-15)) and ((0,5)) (rounded to the nearest integer).

Answer:

A. The graph of (f) is concave up on the open interval(s) ((-20,-15),(0,5))