Question

the graph of ( f ) is given.
(a) on what open intervals is ( f ) increasing?
(b) on what open intervals is ( f ) decreasing?
(c) what are the ( x )-values of the local extrema?
(d) on what open intervals is ( f ) concave up?
(e) on what open intervals is ( f ) concave down?
(f) what are the ( x )-values of the inflection points?
(a) on what open intervals is ( f ) increasing? select the correct choice and, if necessary, fill in the answer
box to complete your choice.
a. the graph of ( f ) is increasing 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.)
b. the graph of ( f ) is not increasing on any open interval

Explanation:

Step1: Recall the increasing function theorem

If \(f^{\prime}(x)>0\) on an open interval \(I\), then \(f(x)\) is increasing on \(I\).
Looking at the graph of \(y = f^{\prime}(x)\), we see that \(f^{\prime}(x)>0\) when \(x<-10\) and \(x > 10\).

Answer:

A. The graph of \(f\) is increasing on the open interval(s) \((-\infty,- 10),(10,\infty)\)