Let y = ƒ(x) be a differentiable function for which the graph of its derivative, ƒ', is given below:
At what x-value(s), if any, does the graph of ƒ have a horizontal tangent?

A)x = 0 only
B)x = -3 only
C)x = 3 only
D)x = -3 and x = 3
E)None

Question

Let y = ƒ(x) be a differentiable function for which the graph of its derivative, ƒ', is given below:
At what x-value(s), if any, does the graph of ƒ have a horizontal tangent?
​
A)x = 0 only
B)x = -3 only
C)x = 3 only
D)x = -3 and x = 3
E)None

Quizplus · Accepted Answer

The graph of ƒ has a horizontal tangent where its derivative, ƒ', equals zero. The given derivative graph crosses the x-axis at x = -3 and x = 3, indicating ƒ' equals zero at these points, hence horizontal tangents at x = -3 and x = 3.

Let Y = ƒ(X) Be a Differentiable Function for Which