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Analyze the function f(x) = x+17 4x +15 if x < 4 if x ≥ 4

Analyze the function f(x) = x+17 4x +15 if x < 4 if x ≥ 4

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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= Analyze the function f(x) = 1/1/x- {. x+17 4x +15 if x < 4 if x ≥ 4
Transcribed Image Text:= Analyze the function f(x) = 1/1/x- {. x+17 4x +15 if x < 4 if x ≥ 4
For continuity, calculate f (4), the left hand limit lim 1 2 x→4- x + 17 the right hand limit lim √4x + 15 x →4+ f(x) = = f(x)-f(4) x-4 For differentiability, you need to compute the left hand limit of √4x + 15 and see whether they are the same or not. You can use that both f(x) = functions and apply our rules for derivatives for these two functions (individually). with f(x) = 1 x f(x)-f(4) x-4 x+17 and ƒ(x) = √4x +15 are differentiable x+17 and the right hand limit of with
Transcribed Image Text:For continuity, calculate f (4), the left hand limit lim 1 2 x→4- x + 17 the right hand limit lim √4x + 15 x →4+ f(x) = = f(x)-f(4) x-4 For differentiability, you need to compute the left hand limit of √4x + 15 and see whether they are the same or not. You can use that both f(x) = functions and apply our rules for derivatives for these two functions (individually). with f(x) = 1 x f(x)-f(4) x-4 x+17 and ƒ(x) = √4x +15 are differentiable x+17 and the right hand limit of with
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