Q1 MULTIPLE CHOICE One answer only If ƒ : (0, 1) → R is differentiable and bounded, then f' is bounded. a. False, here is a counter-example: f(x)=√x. b. True, by mean value theorem. c. False, because (0, 1) is not compact so functions cannot be bounded on that interval. d. True, by definition of the derivative as limħ→0 f(x+h)-f(x) h.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Q1 MULTIPLE CHOICE One answer only
If ƒ : (0, 1) → R is differentiable and bounded, then f' is bounded.
a. False, here is a counter-example: f(x)=√√√x.
b. True, by mean value theorem.
c. False, because (0, 1) is not compact so functions cannot be bounded on that interval.
d. True, by definition of the derivative as limħ→0
ƒ(x+h)-f(x)
h
Transcribed Image Text:Q1 MULTIPLE CHOICE One answer only If ƒ : (0, 1) → R is differentiable and bounded, then f' is bounded. a. False, here is a counter-example: f(x)=√√√x. b. True, by mean value theorem. c. False, because (0, 1) is not compact so functions cannot be bounded on that interval. d. True, by definition of the derivative as limħ→0 ƒ(x+h)-f(x) h
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