Answered: Determine if the following function is…

Determine if the following function is continuous and differentiable at x = 0. ex - sinx 13x² + cos x f(x) = {20.²2²* x < 0. 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.

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...

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Question

Hi-I posted the below question yesterday and received an answer that I am not sure is 100% correct. I follow that the function is continuous, but I calculate that it is also differentiable. I calculate the derivative on both the right and left sides to be = 0. I am not following the answer that I received that says it is not differentiable.

Can you confirm whether the function is differentiable and if not, specifically show the derivative calculation on each side. Thanks.

Determine if the following function is continuous
and differentiable at x = 0.
ex - sin x
f(x) = { 3x² + cos x
x < 0.
x ≥ 0

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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