Problem. Suppose that p() is a differentiable function with d'(1) s ko(1) (k > 0) for t2 a. Multiply both sides by eki, then transpose to show that for i2a. Then apply the mean value theorem to conclude that (1) s pla)eku-a) for t2a.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 52E
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Problem.
Suppose that p() is a differentiable function with
d'(1) s ko(1)
(k > 0)
for t2 a. Multiply both sides by eki, then transpose to
show that
for i2a. Then apply the mean value theorem to conclude
that
(1) s pla)eku-a)
for t2a.
Transcribed Image Text:Problem. Suppose that p() is a differentiable function with d'(1) s ko(1) (k > 0) for t2 a. Multiply both sides by eki, then transpose to show that for i2a. Then apply the mean value theorem to conclude that (1) s pla)eku-a) for t2a.
Expert Solution
Step 1

Given : ϕ'tkϕt   for k>0

To show : for ta    ddtϕte-kt0   and ϕtϕaekt-a

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