Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1. Consider the following function, sin 1(2) - (2²46² (²) ƒ(x): if x = 0 if x = 0 Prove that the function ƒ is differentiable at x = 0 using the definition of (a) (b) Find the formula of the derivative, ƒ'(x) for x ‡ 0, using any differentiation rules you have learned in this course. Indicate clearly which rules are used in your computation. derivatives.

1. Consider the following function, sin 1(2) - (2²46² (²) ƒ(x): if x = 0 if x = 0 Prove that the function ƒ is differentiable at x = 0 using the definition of (a) (b) Find the formula of the derivative, ƒ'(x) for x ‡ 0, using any differentiation rules you have learned in this course. Indicate clearly which rules are used in your computation. derivatives.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 12CR: Determine whether each of the following statements is true or false and explain why. The derivative...
See similar textbooks
icon
Related questions
Question
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 - {27² min (²2) 0 derivatives. ƒ(x) = (a) (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.
Transcribed Image Text: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 - {27² min (²2) 0 derivatives. ƒ(x) = (a) (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.
Expert Solution
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer