suppose that the graph below is the graph of ( f(x) ), the derivative of a function ( f(x) ). find the open…

suppose that the graph below is the graph of ( f(x) ), the derivative of a function ( f(x) ). find the open intervals where ( f(x) ) is a) increasing, or b) decreasing.\n\n a) list any open interval(s) on which ( f(x) ) is increasing. select the correct choice below and, if necessary, fill in the answer box to complete your choices.\n\n a. (type your answer in interval notation. use a comma to separate answers as needed.)\n\n b. the function ( f(x) ) is never increasing.\n\n b) list any open interval(s) on which ( f(x) ) is decreasing. select the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\n a. (type your answer in interval notation. use a comma to separate answers as needed.)\n\n b. the function ( f(x) ) is never decreasing.

suppose that the graph below is the graph of ( f(x) ), the derivative of a function ( f(x) ). find the open intervals where ( f(x) ) is a) increasing, or b) decreasing.\n\n a) list any open interval(s) on which ( f(x) ) is increasing. select the correct choice below and, if necessary, fill in the answer box to complete your choices.\n\n a. (type your answer in interval notation. use a comma to separate answers as needed.)\n\n b. the function ( f(x) ) is never increasing.\n\n b) list any open interval(s) on which ( f(x) ) is decreasing. select the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\n a. (type your answer in interval notation. use a comma to separate answers as needed.)\n\n b. the function ( f(x) ) is never decreasing.

Answer

Explanation:

Step1: Recall the relationship between (f(x)) and (f^{\prime}(x))

If (f^{\prime}(x)>0), then (f(x)) is increasing. If (f^{\prime}(x)<0), then (f(x)) is decreasing.

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

We look for the intervals where (y=f^{\prime}(x)>0). From the graph, (f^{\prime}(x)>0) when (x\in(-\infty, - 8)\cup(8,\infty))

Step3: Analyze the graph of (y = f^{\prime}(x)) for decreasing intervals of (f(x))

We look for the intervals where (y = f^{\prime}(x)<0). From the graph, (f^{\prime}(x)<0) when (x\in(-8,8))

Answer:

a) The function (f(x)) is increasing on the intervals ((-\infty,-8)\cup(8,\infty)) b) The function (f(x)) is decreasing on the interval ((-8,8))