Let f: RR be a function that is differentiable on (a, o), where a is any real constant. Let g: RR be a function defined by g(x) = f(x+1)-f(x). If limx→∞ f'(x) = 0, prove that limx→ 9(x) = 0 by using the Mean Value Theo- rem.
Let f: RR be a function that is differentiable on (a, o), where a is any real constant. Let g: RR be a function defined by g(x) = f(x+1)-f(x). If limx→∞ f'(x) = 0, prove that limx→ 9(x) = 0 by using the Mean Value Theo- rem.
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:Let f: RR be a function that is differentiable on (a, o), where a is any real
constant. Let g: RR be a function defined by
g(x) = f(x + 1) - f(x).
If limx→∞ f'(x) = 0, prove that limo g(x) = 0 by using the Mean Value Theo-
rem.
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