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


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Suppose that p is continuous on (a, c] and differentiable on (a, c), while q is continuous<br>on [c, b) and differentiable on (c, b), let<br>f(x) =<br>f (x) = {P(x), a<x<c<br>l9(х), с <х <b<br>Examine the problem and show that<br>(a) f'(x) = {P'(x), a <x < c<br>lq'(x), c< x <b<br>(b) Under what conditions on p and q does f'(c) exist? Prove that your stated conditions<br>necessary and sufficient.<br>

Extracted 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<><>

Jun 05, 2022
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