Use the Mean Value Theorem to prove: If f(x) and g(x) are differentiable on an interval (a, b) and f'(x) = g'(x) for all x in (a, b), then there is a constant k such that g(x) = f(x) +c for all rin (a, b).
Use the Mean Value Theorem to prove: If f(x) and g(x) are differentiable on an interval (a, b) and f'(x) = g'(x) for all x in (a, b), then there is a constant k such that g(x) = f(x) +c for all rin (a, b).
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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![Use the Mean Value Theorem to prove: If f(x) and g(x) are differentiable on an interval (a, b)
and f'(x) = g'(x) for all x in (a, b), then there is a constant k such that g(x) = f(x) + c for all
x in (a, b).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F606b98dd-813c-4ddf-8b35-b747fa610467%2Fde9d08d3-4827-42f8-ade3-4965a0fc5562%2Fmauk92l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Use the Mean Value Theorem to prove: If f(x) and g(x) are differentiable on an interval (a, b)
and f'(x) = g'(x) for all x in (a, b), then there is a constant k such that g(x) = f(x) + c for all
x in (a, b).
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