Let (f : [0, infinity) -> R be an arbitrary continuous function, which is differentiable on (0,infinity). Assume that (f(0) = 0) and (f’(x) <= 1) for all (x > 0). Show that (f(x) <= x) for all (x > 0).
Let (f : [0, infinity) -> R be an arbitrary continuous function, which is differentiable on (0,infinity). Assume that (f(0) = 0) and (f’(x) <= 1) for all (x > 0). Show that (f(x) <= x) for all (x > 0).
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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Let (f : [0, infinity) -> R be an arbitrary continuous function, which is differentiable on (0,infinity). Assume that (f(0) = 0) and (f’(x) <= 1) for all (x > 0).
Show that (f(x) <= x) for all (x > 0).
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