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1. Consider the following function, if x # 0 if x = 0 Prove that the function f is differentiable at x = 0 using the definition of {a² sin (²3) derivatives. f(x) = (b) Find the formula of the derivative, f'(x) for x = 0, using any differentiation rules you have learned in this course. Indicate clearly which rules are used in your computation. Note: after this work, you may want to see if the derivative function is continuous at x = 0. While the original function f is differentiable and so also continuous at x = 0, its derivative is not continuous at x = 0.

1. Consider the following function, if x # 0 if x = 0 Prove that the function f is differentiable at x = 0 using the definition of {a² sin (²3) derivatives. f(x) = (b) Find the formula of the derivative, f'(x) for x = 0, using any differentiation rules you have learned in this course. Indicate clearly which rules are used in your computation. Note: after this work, you may want to see if the derivative function is continuous at x = 0. While the original function f is differentiable and so also continuous at x = 0, its derivative is not continuous at x = 0.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Consider the following function, {a² sin (²3) derivatives. if x # 0 if x = 0 Prove that the function f is differentiable at x = 0 using the definition of (b) Find the formula of the derivative, f'(x) for x = 0, using any differentiation rules you have learned in this course. Indicate clearly which rules are used in your computation. f(x) = Note: after this work, you may want to see if the derivative function is continuous at x = 0. While the original function f is differentiable and so also continuous at x = 0, its derivative is not continuous at x = 0.
Transcribed Image Text:1. Consider the following function, {a² sin (²3) derivatives. if x # 0 if x = 0 Prove that the function f is differentiable at x = 0 using the definition of (b) Find the formula of the derivative, f'(x) for x = 0, using any differentiation rules you have learned in this course. Indicate clearly which rules are used in your computation. f(x) = Note: after this work, you may want to see if the derivative function is continuous at x = 0. While the original function f is differentiable and so also continuous at x = 0, its derivative is not continuous at x = 0.
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