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.
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. ​  ​  ​
D) , 
E) , ,

Quizplus · Accepted Answer

Points of inflection occur where the second derivative changes sign. From the graph, we can see that the function changes from concave up (positive second derivative) to concave down (negative second derivative) at x ≈ 1.2 and from concave down to concave up at x ≈ 5.5. Therefore, the points of inflection are (1.2, -5.5) and (5.5, 1.5), which corresponds to choice D.

A Function and Its Graph Are Given