The function f (x) is defined by the rule x2 +1 if x < 2 f (x) = if x = 2 %3D 4x – 3 if x > 2 - a) Calculate the left derivative and the right derivative of f at x = 2. You must use the limit definition because we did not establish rules for calculating one sided derivatives. b) Write a piecewise function for the derivative of f at all points in R.

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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. The function f (x) is defined by the rule
x? +1 if æ < 2
f (x) =
5
if æ = 2
4x – 3 if x > 2
(a) Calculate the left derivative and the right derivative of f at
x = 2.
You must use the limit definition because we did not
establish rules for calculating one sided derivatives.
b) Write a piecewise function for the derivative of f at all points in
R.
||
Transcribed Image Text:. The function f (x) is defined by the rule x? +1 if æ < 2 f (x) = 5 if æ = 2 4x – 3 if x > 2 (a) Calculate the left derivative and the right derivative of f at x = 2. You must use the limit definition because we did not establish rules for calculating one sided derivatives. b) Write a piecewise function for the derivative of f at all points in R. ||
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