2) Let f becontinuous on [a, b], differentiable on(a, b) and positive (i.e., > 0) for all x = (a, b).Prove that there exists c = (a, b) such thatf'(c)1=+ (Hint: consider the function●f(c) a-cb-cF(x) = (x − a) (x − b) ƒ (x) and use MVT forF(x) to show the existence of such c = (a, b).)

Given f be continuous on [a,b] and differentiable on (a,b) and positive for all x∈(a,b)

2) Let f be continuous on [a, b], differentiable on (a, b) and positive (i.e., > 0) for all x ≤ (a, b). Prove that there exists c € (a, b) such that f'(c) 1 = f(c) a-c + b²c. (Hint: consider the function F(x) = (x − a) (x − b) ƒ (x) and use MVT for F(x) to show the existence of such c = (a, b).)

2) Let f be continuous on [a, b], differentiable on (a, b) and positive (i.e., > 0) for all x ≤ (a, b). Prove that there exists c € (a, b) such that f'(c) 1 = f(c) a-c + b²c. (Hint: consider the function F(x) = (x − a) (x − b) ƒ (x) and use MVT for F(x) to show the existence of such c = (a, b).)

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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