Let f(x) be differentiable on R. Suppose f(0) = A > 0 and lim f(x) = lim f(x)=0 1. Show that f(x) achieves its maximum on R. 2. Show that there exists c E R such that f'(c) = 0.
Let f(x) be differentiable on R. Suppose f(0) = A > 0 and lim f(x) = lim f(x)=0 1. Show that f(x) achieves its maximum on R. 2. Show that there exists c E R such that f'(c) = 0.
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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Transcribed Image Text:Let f(x) be differentiable on R. Suppose f(0) = A >0 and
lim f(x) = lim f(x)=0
1.
Show that f() achieves its maximum on R.
2.
Show that there exists c E R such that f'(c) = 0.
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