A function and its graph are given.Use the second derivative to locate all x-values of points of inflection on the graph of Check these results against the graph shown.

A)
B)
C)
D) ,
E) , ,

Question

​A function and its graph are given.Use the second derivative to locate all x-values of points of inflection on the graph of  Check these results against the graph shown. ​
​  ​  ​
A) ​ 
B) ​ 
C) ​ 
D) ​ , 
E) ​ , ,

Quizplus · Accepted Answer

- Points of inflection occur where the concavity changes, which means it's a local maximum or minimum of the second derivative (i.e. where the second derivative crosses the x-axis).
- From the second derivative graph, we can see that it crosses the x-axis at two points: approximately -4.4 and 1.2. 
- These correspond to the points of inflection on the original function at approximately x = -4.4 and x = 1.2. 
- Choice D lists these two x-values correctly. The other choices either miss one of the points or include extra points that are not points of inflection.

​A Function and Its Graph Are Given

A Function and Its Graph Are Given