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QUESTION 3 Suppose f: R→ R satisfies |f(x)| = |x| for all X. Which of the following is true? Of must be differentiable at 0. Some, but not all, such f are differentiable at 0. If we assume that f is continuous at 0, then it necessarily follows that f is differentiable at 0. O Some, but not all, such f are differentiable at O. If we assume that f is continuous at 0, it does not necessarily follow that f is differentiable at 0. O f must not be differentiable at 0.

QUESTION 3 Suppose f: R→ R satisfies |f(x)| = |x| for all X. Which of the following is true? Of must be differentiable at 0. Some, but not all, such f are differentiable at 0. If we assume that f is continuous at 0, then it necessarily follows that f is differentiable at 0. O Some, but not all, such f are differentiable at O. If we assume that f is continuous at 0, it does not necessarily follow that f is differentiable at 0. O f must not be differentiable at 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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QUESTION 3 Suppose f: R→ R satisfies |f(x)| = |x| for all X. Which of the following is true? Of must be differentiable at 0. Some, but not all, such f are differentiable at 0. If we assume that f is continuous at 0, then it necessarily follows that f is differentiable at 0. O Some, but not all, such f are differentiable at O. If we assume that f is continuous at 0, it does not necessarily follow that f is differentiable at 0. O f must not be differentiable at 0.
Transcribed Image Text:QUESTION 3 Suppose f: R→ R satisfies |f(x)| = |x| for all X. Which of the following is true? Of must be differentiable at 0. Some, but not all, such f are differentiable at 0. If we assume that f is continuous at 0, then it necessarily follows that f is differentiable at 0. O Some, but not all, such f are differentiable at O. If we assume that f is continuous at 0, it does not necessarily follow that f is differentiable at 0. O f must not be differentiable at 0.
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