Suppose f is defined on [a, b] and g is defined on [b, c] with f(b) g(b). Then define { f(x) if a < x < b, h(x) = g(x) if b
Suppose f is defined on [a, b] and g is defined on [b, c] with f(b) g(b). Then define { f(x) if a < x < b, h(x) = g(x) if b
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
![Suppose f is defined on [a, b] and g is defined on [b, c] with f(b) =
g(b). Then define
f(z)
if a <r < b,
h(x) = { glz)
if b< r < c.
Give an example where f and g are differentiable but h is not.
Give a definition of one-sided derivatives f' (b) and g'(b) and show
that the equality of these is a necessary and sufficient condition
for h to be differentiable, given that f and g are differentiable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2d11cad-adcc-47c8-9f66-91db37982b76%2F41df32b1-8572-4c4e-af0d-6e175a2b78a6%2Fqens1a5_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose f is defined on [a, b] and g is defined on [b, c] with f(b) =
g(b). Then define
f(z)
if a <r < b,
h(x) = { glz)
if b< r < c.
Give an example where f and g are differentiable but h is not.
Give a definition of one-sided derivatives f' (b) and g'(b) and show
that the equality of these is a necessary and sufficient condition
for h to be differentiable, given that f and g are differentiable.
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