For the graphed function below, state the x-values for which the derivative does not exist.
A) x = 4, - 4
B) x = 0, 2, - 2
C) x = 2, - 2
D) x = 0, 4, - 4

Question

For the graphed function below, state the x-values for which the derivative does not exist. 
A) x = 4, - 4 
B) x = 0, 2, - 2 
C) x = 2, - 2 
D) x = 0, 4, - 4

Quizplus · Accepted Answer

The derivative does not exist at points where the function has a sharp turn or corner. From the graph, we can see that the function has sharp turns at x = 2 and x = -2, so the derivative does not exist at these points. The function also has a vertical tangent line at x = 0, so the derivative does not exist at this point as well. Therefore, the best choice is C, which lists x = 2 and x = -2 as the points where the derivative does not exist.

For the Graphed Function Below, State the X-Values for Which