Question

hw9 the derivative as a function (targets l6, d1, d2; §3.2)
score: 8/9 answered: 8/9
question 9
select all the points at which the graph above is not differentiable
□ - 4
□ - 3
□ - 2
□ - 1
□ 0
□ 1
□ 2
□ 3
□ 4

Explanation:

Step1: Recall non - differentiability conditions

A function is not differentiable at a point if there is a sharp corner, a cusp, a vertical tangent, or a discontinuity at that point.

Step2: Analyze the graph

• At \(x=-2\), there is a sharp corner. The slope of the left - hand side and the right - hand side of the function at \(x = - 2\) are different, so the derivative does not exist.
• At \(x = 0\), there is a discontinuity (a hole in the graph). Since the function is not continuous at \(x=0\), it is not differentiable at \(x = 0\).
• At \(x=3\), there is a vertical tangent. As the slope of the tangent line approaches infinity at \(x = 3\), the function is not differentiable at this point.

Answer:

-2, 0, 3