Suppose that p is continuous on (a, c] and differentiable on (a, c), while q is continuous on [c, b) and differentiable on (c, b), let SP(x), a < x < c lq(x), c< x

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Suppose that p is continuous on (a, c] and differentiable on (a, c), while q is continuous
on [c, b) and differentiable on (c, b), let
f(x) =
f (x) = {P(x), a<x<c
l9(х), с <х <b
Examine the problem and show that
(a) f'(x) = {P'(x), a <x < c
lq'(x), c< x <b
(b) Under what conditions on p and q does f'(c) exist? Prove that your stated conditions
necessary and sufficient.
Transcribed Image Text:Suppose that p is continuous on (a, c] and differentiable on (a, c), while q is continuous on [c, b) and differentiable on (c, b), let f(x) = f (x) = {P(x), a<x<c l9(х), с <х <b Examine the problem and show that (a) f'(x) = {P'(x), a <x < c lq'(x), c< x <b (b) Under what conditions on p and q does f'(c) exist? Prove that your stated conditions necessary and sufficient.
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