Suppose that f : R -R is differentiable at z = 0. (a) Prove that (t) lim,-o EA = f'(0) (b) Give an example of a function g for which the limit in (t) exists but which is not differentiable at Z= 0.
Suppose that f : R -R is differentiable at z = 0. (a) Prove that (t) lim,-o EA = f'(0) (b) Give an example of a function g for which the limit in (t) exists but which is not differentiable at Z= 0.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Transcribed Image Text:Suppose that f : R +R is differentiable at z = 0.
(a) Prove that (t) lim,-o EA = f'(0)
(b) Give an example of a function g for which the limit in (t) exists but which is not differentiable at
Z= 0.
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