(2342) 4. Let f: RR. f(x + h) = f(x)f(h) and f(0) #0. Prove that (a) f(0) = 1 and (b) if f'(0) exists, then f'(x) does exist for all a E R and f'(x) = f(x). f'(0)

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.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...
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4. Let f : R → R. f(x + h) = f(x)f(h) and f(0) ≠ 0. Prove that
(a) f(0) = 1 and
(b) if f'(0) exists, then f'(x) does exist for all x ∈ Rand f'(x) = f(x) - f'(0).
Transcribed Image Text:(42) 4. Let f : R → R. f(x + h) = f(x)f(h) and f(0) ≠ 0. Prove that (a) f(0) = 1 and (b) if f'(0) exists, then f'(x) does exist for all x ∈ Rand f'(x) = f(x) - f'(0).
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