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