Let f: [a, b] → R be differentiable and that m≤ f'(x) ≤M for all x € [a, b]. (b) Let x € [a, b]. Show that f(a) +m(x-a) ≤ f(x) ≤ f(a) + M(x -a). (c) Suppose that g: [0,5] → R be differentiable, g(0) = 0, and that that -3 ≤ g'(x) ≤ 3, use part (b), to show that -5x ≤ g(x) ≤ 5z.

Let f: [a, b] → R be differentiable and that m≤ f'(x) ≤M for all x € [a, b]. (b) Let x € [a, b]. Show that f(a) +m(x-a) ≤ f(x) ≤ f(a) + M(x -a). (c) Suppose that g: [0,5] → R be differentiable, g(0) = 0, and that that -3 ≤ g'(x) ≤ 3, use part (b), to show that -5x ≤ g(x) ≤ 5z.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 30EQ

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