Suppose f is continuously differentiable on an interval (a, b). Prove that on any closed subinterval [c, d] the function is uniformly dif- ferentiable in the sense that given any 1/n there exists 1/m (inde- pendent of ro) such that |f(x)- f(xo)-f'(x0)(x-x0)|< lx-xo|/n whenever x – xol < 1/m. (Hint: use the mean value theorem and the uniform continuity of f' on [c, d].)

Suppose f is continuously differentiable on an interval (a, b). Prove that on any closed subinterval [c, d] the function is uniformly dif- ferentiable in the sense that given any 1/n there exists 1/m (inde- pendent of ro) such that |f(x)- f(xo)-f'(x0)(x-x0)|< lx-xo|/n whenever x – xol < 1/m. (Hint: use the mean value theorem and the uniform continuity of f' on [c, d].)

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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