In this problem, and its graph are given. Use the graph of to determine where has a point of inflection.
E)no point of inflection

Question

In this problem,  and its graph are given. Use the graph of  to determine where  has a point of inflection. ​   ​
E)no point of inflection

Quizplus · Accepted Answer

A point of inflection occurs when the concavity of the function changes. From the graph of 11eb0d3b_9865_9e28_9790_7fa775b8c1d4_TB1243_11, we can see that the function is concave up on the interval (−∞,−2] and concave down on the interval [−2,0]. Therefore, we know that 11eb0d3b_9865_9e2a_9790_8509d8a06e9b_TB1243_11 must have a point of inflection somewhere in the interval [−2,0]. Looking at the graph of 11eb0d3b_9865_9e29_9790_d59af72aa7cc_TB1243_11, we can see that the graph changes from concave down to concave up around x = −1.5, which is in the interval [−2,0]. Therefore, the point of inflection for 11eb0d3b_9865_9e2a_9790_8509d8a06e9b_TB1243_11 is at approximately x = −1.5, which corresponds to choice (C).

In This Problem, and Its Graph Are Given