Question

(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

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) \((-10,5)\)