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Let a E R. Let f be a function. Assume f is differentiable at a. 1 Assume f is never 0. Let g be the function defined by the equation g(x)% = f(x) %3D -f (a) f(a)? Write a proof directly from the definition of derivative, without using any of the differentiation Prove that g is differentiable at a and that g'(a) = %3D

Let a E R. Let f be a function. Assume f is differentiable at a. 1 Assume f is never 0. Let g be the function defined by the equation g(x)% = f(x) %3D -f (a) f(a)? Write a proof directly from the definition of derivative, without using any of the differentiation Prove that g is differentiable at a and that g'(a) = %3D

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 32EQ
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C. MAT1 O conter lineara G mutate P lineara 137 20 13 O (3) 3.4 u lesson7 Crowc G barti th.toronto.edu/alfonso/137/PS/137_2021_A3.pdf Acorn - University o... Quercus Mail - Christophe.. E MAT 137: Calculus... ΜΑΤ223 PHY131H1F - Classes are taking those steps, justify everything you do. Explain explicitly anything you do that is not merely a straightforward algebraic manipulation. If you are using a hypotheses, say so explicitly. If you are invoking a theorem, a property, or a previously proven claim, say so explicitly (and make sure you know you are allowed to use it). We want you to be very conscious of everything you are using and everything you are assuming. 2. Let a E R. Let f be a function. Assume f is differentiable at a. | 1 Assume f is never 0. Let g be the function defined by the equation g(x) f (x) – f'(a) f (a)? Prove that g is differentiable at a and that g (a) = Write a proof directly from the definition of derivative, without using any of the differentiation rules.
Transcribed Image Text:C. MAT1 O conter lineara G mutate P lineara 137 20 13 O (3) 3.4 u lesson7 Crowc G barti th.toronto.edu/alfonso/137/PS/137_2021_A3.pdf Acorn - University o... Quercus Mail - Christophe.. E MAT 137: Calculus... ΜΑΤ223 PHY131H1F - Classes are taking those steps, justify everything you do. Explain explicitly anything you do that is not merely a straightforward algebraic manipulation. If you are using a hypotheses, say so explicitly. If you are invoking a theorem, a property, or a previously proven claim, say so explicitly (and make sure you know you are allowed to use it). We want you to be very conscious of everything you are using and everything you are assuming. 2. Let a E R. Let f be a function. Assume f is differentiable at a. | 1 Assume f is never 0. Let g be the function defined by the equation g(x) f (x) – f'(a) f (a)? Prove that g is differentiable at a and that g (a) = Write a proof directly from the definition of derivative, without using any of the differentiation rules.
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