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 (y = f(x)) occur where (f^{\prime}(x)=0) or (f^{\prime}(x)) is undefined.

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

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

Answer:

The (x) - values of the points where (f^{\prime}(x) = 0) (read from the graph of (y=f^{\prime}(x))). Without seeing the actual graph values, we can't give specific numbers. But in general, if the graph of (y = f^{\prime}(x)) crosses the (x) - axis at (x=a,x = b,x = c), the critical points are (x=a,b,c).