the graph of ( f ) is given.\n(a) on what open intervals is ( f ) increasing?\n(b) on what open intervals is…

the graph of ( f ) is given.\n(a) on what open intervals is ( f ) increasing?\n(b) on what open intervals is ( f ) decreasing?\n(c) what are the values of\n(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.\na. the graph of ( f ) is concave up on the open interval(s) (square).\n(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

the graph of ( f ) is given.\n(a) on what open intervals is ( f ) increasing?\n(b) on what open intervals is ( f ) decreasing?\n(c) what are the values of\n(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.\na. the graph of ( f ) is concave up on the open interval(s) (square).\n(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

The function (y = f(x)) is concave up when (f^{\prime\prime}(x)>0). Since (f^{\prime\prime}(x)) is the derivative of (f^{\prime}(x)), we need to find where (f^{\prime}(x)) is increasing.

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

Looking at the graph of (y = f^{\prime}(x)), we observe that (f^{\prime}(x)) is increasing on the intervals ((- \infty,- 4)) and ((12,\infty)) (by visually inspecting the slope of (f^{\prime}(x)) which represents (f^{\prime\prime}(x))).

Answer:

((-\infty,-4),(12,\infty))