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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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