Consider a function f whose domain is the interval [a, b]. Show that if |f(x) − f(y)| ≤ (x − y)², for all x, y € [a, b], then f is a constant function.
Consider a function f whose domain is the interval [a, b]. Show that if |f(x) − f(y)| ≤ (x − y)², for all x, y € [a, b], then f is a constant function.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 51E
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![Consider a function f whose domain is the interval [a, b]. Show that if
f(x)-f(y)| ≤ (x - y)²,
for all r, y € [a, b], then f is a constant function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e5f8f6e-6110-48ea-bb72-f3111af272da%2F3a29a6e1-353b-40f5-a87a-86b766f03b9d%2F8h483f_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a function f whose domain is the interval [a, b]. Show that if
f(x)-f(y)| ≤ (x - y)²,
for all r, y € [a, b], then f is a constant function.
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