use the graph of f and f to find the critical points and inflection points of f, the intervals on which f is…

use the graph of f and f to find the critical points and inflection points of f, the intervals on which f is increasing and decreasing, and the intervals of concavity. then, graph f assuming f(0)=0. find the critical points. the critical points are x = _. (use a comma to separate answers as needed.)

use the graph of f and f to find the critical points and inflection points of f, the intervals on which f is increasing and decreasing, and the intervals of concavity. then, graph f assuming f(0)=0. find the critical points. the critical points are x = _. (use a comma to separate answers as needed.)

Answer

Explanation:

Step1: Recall critical - point definition

Critical points of a function (y = f(x)) occur where (f^{\prime}(x)=0) or (f^{\prime}(x)) is undefined.

Step2: Identify (x) - values from (y = f^{\prime}(x)) graph

From the graph of (y = f^{\prime}(x)), find the (x) - values where (y = f^{\prime}(x)=0). These are the (x) - intercepts of the (y = f^{\prime}(x)) graph.

Answer:

The critical points are the (x) - values where the graph of (y = f^{\prime}(x)) crosses the (x) - axis. From the given graph (assuming the (x) - intercepts are at (x = 3,6,9,12)), (x = 3,6,9,12)