Function $f$ is graphed. The dashed lines represent asymptotes.

Select all the $x$-values for which $f$ is not differentiable.
Choose all answers that apply:
A -3
B 0
C 1

D 3

Question

Function $f$ is graphed. The dashed lines represent asymptotes.

Select all the $x$-values for which $f$ is not differentiable.
Choose all answers that apply:
A -3
B 0
C 1

D 3

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the points where the function $f$ is not differentiable. These points typically include discontinuities, sharp corners, and vertical tangents. ‖ ‖ step 2 ⋮ From the graph, observe the following: - At $x = -3$, there is a vertical asymptote, indicating a discontinuity. - At $x = 0$, the function reappears above the horizontal asymptote, indicating a discontinuity. - At $x = 1$, there is a hollow blue dot, indicating a discontinuity. - At $x = 3$, there is a peak, which might indicate a sharp corner. ‖ ‖ step 3 ⋮ Conclude that the function $f$ is not differentiable at $x = -3$, $x = 0$, and $x = 1$. ‖ ***A, B, C*** ∻Key Concept∻ ⚹Non-differentiability points⚹ ∻Explanation∻ ⚹A function is not differentiable at points of discontinuity, sharp corners, and vertical tangents.⚹◊What criteria can be used to determine if a function is differentiable at a specific point?⍭ Generate me a similar question◊

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