yf- 16y = z– 4z?. Use implicit differentiation to find the equation of the tangent line to the graph at the point (2, 4). Student solution. We begin by differentiation and obtain After we simplify as much as possible we obtain the derivative dy dr The slope of the tangent line at (2, 4) equals m= The equation of the tangent line at (2, 4) is given by

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 following curve defined by the equation
f- 16y = z – 4z².
Use implicit differentiation to find the equation of the tangent line to the graph at the point (2, 4).
Student solution.
We begin by differentiation and obtain
After we simplify as much as possible we obtain the derivative
dz
The slope of the tangent line at (2, 4) equals
m%3D
The equation of the tangent line at (2, 4) is given by
Transcribed Image Text:Consider the following curve defined by the equation f- 16y = z – 4z². Use implicit differentiation to find the equation of the tangent line to the graph at the point (2, 4). Student solution. We begin by differentiation and obtain After we simplify as much as possible we obtain the derivative dz The slope of the tangent line at (2, 4) equals m%3D The equation of the tangent line at (2, 4) is given by
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