2. (a) Assume that (a, b) is a bounded open interval in R. Using Mean Value Theorem, prove that if f: (a, b) → R is an unbounded differentiable function (i.e., for every M > 0 there exists x e (a, b) such that |f(x)| > M), then f' is also an unbounded function.
2. (a) Assume that (a, b) is a bounded open interval in R. Using Mean Value Theorem, prove that if f: (a, b) → R is an unbounded differentiable function (i.e., for every M > 0 there exists x e (a, b) such that |f(x)| > M), then f' is also an unbounded function.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2a and b please
Transcribed Image Text:(a) Assume that (a, b) is a bounded open interval in R. Using Mean Value Theorem, prove
that if f: (a, b) → R is an unbounded differentiable function (i.e., for every M > 0 there
exists x e (a, b) such that |f(x)| > M), then f' is also an unbounded function.
(b) Give an example of a function f: (a, b) → R, where (a, b) is a bounded open real
interval, such that f is differentiable on (a, b), f' is unbounded on (a, b), but f is
bounded function on (a, b).
2.
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