For the given function and graph, determine all critical value(s), where .
D) and
E) and and

Question

For the given function and graph, determine all critical value(s), where  . ​  ​ 
D) and 
E) and and

Quizplus · Accepted Answer

Critical values are the points on the graph where the function experiences a change in concavity, or a local extrema (minimums or maximums). The critical values are the points where the derivative of the function is equal to zero or undefined. 
From the graph, we can see that the function has local maximums at points A and B, and a local minimum at point C. Therefore, we need to find where the derivative is zero or undefined. 
The derivative is zero or undefined at points where the graph has a vertical tangent or a cusp. From the graph, we see that at points D and E, the graph has a vertical tangent, therefore the derivative is undefined at these points, making them critical values. 
Thus, the correct answer is D.

For the Given Function and Graph, Determine All Critical Value(s)