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EXAMPLE 3.1.1 Find the equation of the tangent line to the graph of f() = x² at z = 2 . Solution m = lim 72 + h)– f(2) h (2 + h)² – 4 lim h = lim A-0 4+4h + h?-4 = lim h(4 + h) lim(4 + h) = 4 h m=4 , x=2 y = m(x – a) + f(a) y = 4(x – 2) + 4 y = 4z – 4 %3D

EXAMPLE 3.1.1 Find the equation of the tangent line to the graph of f() = x² at z = 2 . Solution m = lim 72 + h)– f(2) h (2 + h)² – 4 lim h = lim A-0 4+4h + h?-4 = lim h(4 + h) lim(4 + h) = 4 h m=4 , x=2 y = m(x – a) + f(a) y = 4(x – 2) + 4 y = 4z – 4 %3D

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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EXAMPLE 3.1.1 Find the equation of the tangent line to the graph of f(z) = 2² at z = 2. Solution (2 + h)° – 4 m = lim (2 + h)– $(2) = lim h 4+ 4h + h?-4 = lim h(4 + h) = lim(4 + h) = 4 = lim h m=4 , x=2 y = m(x – a) + f(a) y = 4(x – 2) + 4 y = 4x – 4 %3D
Transcribed Image Text:EXAMPLE 3.1.1 Find the equation of the tangent line to the graph of f(z) = 2² at z = 2. Solution (2 + h)° – 4 m = lim (2 + h)– $(2) = lim h 4+ 4h + h?-4 = lim h(4 + h) = lim(4 + h) = 4 = lim h m=4 , x=2 y = m(x – a) + f(a) y = 4(x – 2) + 4 y = 4x – 4 %3D
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