Suppose that a, b E R and that a < b. Suppose also that f is continuous on [a, b] and differentiable on (a, b). Suppose also that for all y = (a, b) we have f'(y) #1. Prove that there exists at most one point x = (a, b) so that f(x) = x. [Hint: Suppose that there are two such points which are different, so f(x)= x and f(z) = z. What does the Mean Value Theorem say?]

Suppose that a, b E R and that a < b. Suppose also that f is continuous on [a, b] and differentiable on (a, b). Suppose also that for all y = (a, b) we have f'(y) #1. Prove that there exists at most one point x = (a, b) so that f(x) = x. [Hint: Suppose that there are two such points which are different, so f(x)= x and f(z) = z. What does the Mean Value Theorem say?]

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter8: Further Techniques And Applications Of Integration

Section8.2: Integration By Parts

Problem 44E

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