1. Consider the following function, (a) [x² sin (²) if x #0 f(x) = { +) - ( ²³² (²) if x = 0 derivatives. 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. 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, (a) [x² sin (²) if x #0 f(x) = { +) - ( ²³² (²) if x = 0 derivatives. 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. 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 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.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 35E

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