Suppose that there exists M> 0 and 8 >0 such that for all r = (a −8, a+6) \ {a}, f(x) = f(a)| ≤ Mx - aª. Show that when a > 1, then f is differentiable at a and when a > 0, f is continuous at a.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 11E
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Suppose that there exists M> 0 and 8 >0 such that for all r = (a −8, a+6) \ {a},
f(x) = f(a)| ≤ Mx - aª.
Show that when a > 1, then f is differentiable at a and when a > 0, f is continuous at a.
Transcribed Image Text:Suppose that there exists M> 0 and 8 >0 such that for all r = (a −8, a+6) \ {a}, f(x) = f(a)| ≤ Mx - aª. Show that when a > 1, then f is differentiable at a and when a > 0, f is continuous at a.
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