(d) on what open intervals is f concave up? select the correct choice and, if necessary, fill in the answer…

(d) on what open intervals is f concave up? select the correct choice and, if necessary, fill in the answer box to complete your choice. a. the graph of f is concave up on the open interval(s) (-10,5) (type your answer in interval notation. round to the nearest integer as needed. use a comma to separate answers as needed.) b. the graph of f is not concave up on any open interval

(d) on what open intervals is f concave up? select the correct choice and, if necessary, fill in the answer box to complete your choice. a. the graph of f is concave up on the open interval(s) (-10,5) (type your answer in interval notation. round to the nearest integer as needed. use a comma to separate answers as needed.) b. the graph of f is not concave up on any open interval

Answer

Explanation:

Step1: Recall the concavity rule

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

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

Looking at the graph of (y = f^{\prime}(x)), we observe the intervals where (y = f^{\prime}(x)) is increasing. From the graph, we can see that the function (y = f^{\prime}(x)) is increasing on the interval ((- 10,5)).

Answer:

A. The graph of (f) is concave up on the open interval(s) ((-10,5))