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• Consider the function f (x) = |3x – 6. Graph the function, either a quick sketch by hand or using technology. o For what value(s) of x is f (x) not differentiable? Explain using your observations of the graph. o How is differentiability related to limits? o Rewrite f (x) as a piecewise function. o Use the limit definition of the derivative and the piecewise representation of f (x) to confirm your observations about differentiability from the graph. Be sure to tell me the story of how you choose what limits you do and why!

• Consider the function f (x) = |3x – 6. Graph the function, either a quick sketch by hand or using technology. o For what value(s) of x is f (x) not differentiable? Explain using your observations of the graph. o How is differentiability related to limits? o Rewrite f (x) as a piecewise function. o Use the limit definition of the derivative and the piecewise representation of f (x) to confirm your observations about differentiability from the graph. Be sure to tell me the story of how you choose what limits you do and why!

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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• Consider the function f (x) = |3x – 6. Graph the function, either a quick sketch by hand or using technology. o For what value(s) of x is f (x) not differentiable? Explain using your observations of the graph. o How is differentiability related to limits? o Rewrite f (x) as a piecewise function. o Use the limit definition of the derivative and the piecewise representation of f (x) to confirm your observations about differentiability from the graph. Be sure to tell me the story of how you choose what limits you do and why!
Transcribed Image Text:• Consider the function f (x) = |3x – 6. Graph the function, either a quick sketch by hand or using technology. o For what value(s) of x is f (x) not differentiable? Explain using your observations of the graph. o How is differentiability related to limits? o Rewrite f (x) as a piecewise function. o Use the limit definition of the derivative and the piecewise representation of f (x) to confirm your observations about differentiability from the graph. Be sure to tell me the story of how you choose what limits you do and why!
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