Suppose f(x) = x. g(x) for some function g. Which of the following is true? Of need not be differentiable at 0. If we suppose furthermore that g is continuous at 0, it still does not follow that f is differentiable at 0. If we suppose furthermore that g is differentiable at 0, then it follows that f is differentiable at 0. Of must be differentiable at 0. Of need not be differentiable at O. If we suppose furthermore that g is continuous at 0, it still does not follow that f is differentiable at 0. If we suppose furthermore that g is differentiable at 0, then it still does not follow that f is differentiable at 0. Of need not be differentiable at O. If we suppose furthermore that g is continuous at 0, then it follows that f is differentiable at 0.
Suppose f(x) = x. g(x) for some function g. Which of the following is true? Of need not be differentiable at 0. If we suppose furthermore that g is continuous at 0, it still does not follow that f is differentiable at 0. If we suppose furthermore that g is differentiable at 0, then it follows that f is differentiable at 0. Of must be differentiable at 0. Of need not be differentiable at O. If we suppose furthermore that g is continuous at 0, it still does not follow that f is differentiable at 0. If we suppose furthermore that g is differentiable at 0, then it still does not follow that f is differentiable at 0. Of need not be differentiable at O. If we suppose furthermore that g is continuous at 0, then it follows that f is differentiable at 0.
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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Transcribed Image Text:Suppose f(x) = x. g(x) for some function g. Which of the following is true?
Of need not be differentiable at 0. If we suppose furthermore that g is continuous at 0, it still does not follow that f is differentiable
at 0. If we suppose furthermore that g is differentiable at 0, then it follows that f is differentiable at 0.
Of must be differentiable at 0.
Of need not be differentiable at O. If we suppose furthermore that g is continuous at 0, it still does not follow that f is differentiable
at 0. If we suppose furthermore that g is differentiable at 0, then it still does not follow that f is differentiable at 0.
Of need not be differentiable at O. If we suppose furthermore that g is continuous at 0, then it follows that f is differentiable at 0.
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