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For the following graph of f(x), identify where f(x) is not differentiable and why. -5 -4 2- 3 4 X f(x) is not differentiable at x = 0 because f(x) is not defined at x = 0. f(x) is not differentiable at x = 0 because f(x) has a corner at x = 0. f(x) is not differentiable at x = 0 because f(x) has a cusp at x = 0. Of(x) is not differentiable at x = 0 because f(x) has a jump at x = 0.

For the following graph of f(x), identify where f(x) is not differentiable and why. -5 -4 2- 3 4 X f(x) is not differentiable at x = 0 because f(x) is not defined at x = 0. f(x) is not differentiable at x = 0 because f(x) has a corner at x = 0. f(x) is not differentiable at x = 0 because f(x) has a cusp at x = 0. Of(x) is not differentiable at x = 0 because f(x) has a jump at x = 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For the following graph of \( f(x) \), identify where \( f(x) \) is not differentiable and why. **Graph Explanation:** The graph shows a function \( f(x) \) plotted in the Cartesian plane with the x-axis ranging from -5 to 5 and the y-axis from -4 to 4. The function appears to approach the y-axis but is not defined at \( x = 0 \), as there is a gap indicating a discontinuity. The curve on the left approaches \( x = 0 \) from the negative side, moving downwards and sharply turning upwards as it approaches zero. From the positive side, the function approaches zero from above. This indicates a discontinuity at \( x = 0 \). **Options:** - \( \circ \) \( f(x) \) is not differentiable at \( x = 0 \) because \( f(x) \) is not defined at \( x = 0 \). - \( \circ \) \( f(x) \) is not differentiable at \( x = 0 \) because \( f(x) \) has a corner at \( x = 0 \). - \( \circ \) \( f(x) \) is not differentiable at \( x = 0 \) because \( f(x) \) has a cusp at \( x = 0 \). - \( \circ \) \( f(x) \) is not differentiable at \( x = 0 \) because \( f(x) \) has a jump at \( x = 0 \).
Transcribed Image Text:For the following graph of \( f(x) \), identify where \( f(x) \) is not differentiable and why. **Graph Explanation:** The graph shows a function \( f(x) \) plotted in the Cartesian plane with the x-axis ranging from -5 to 5 and the y-axis from -4 to 4. The function appears to approach the y-axis but is not defined at \( x = 0 \), as there is a gap indicating a discontinuity. The curve on the left approaches \( x = 0 \) from the negative side, moving downwards and sharply turning upwards as it approaches zero. From the positive side, the function approaches zero from above. This indicates a discontinuity at \( x = 0 \). **Options:** - \( \circ \) \( f(x) \) is not differentiable at \( x = 0 \) because \( f(x) \) is not defined at \( x = 0 \). - \( \circ \) \( f(x) \) is not differentiable at \( x = 0 \) because \( f(x) \) has a corner at \( x = 0 \). - \( \circ \) \( f(x) \) is not differentiable at \( x = 0 \) because \( f(x) \) has a cusp at \( x = 0 \). - \( \circ \) \( f(x) \) is not differentiable at \( x = 0 \) because \( f(x) \) has a jump at \( x = 0 \).
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