Implicitly differentiate the equation y? + 4xy +x In 2x = 0. Isolate y' in the resulting equation. Use the result to find the equations of the tangent lines to the graph of this equation at the points (,0) and (;,-2). Convert both tangent line equations to the slope-intercept form y = mx + b.

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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Implicitly differentiate the equation \( y^2 + 4xy + x \ln 2x = 0 \). Isolate \( y' \) in the resulting equation. Use the result to find the equations of the tangent lines to the graph of this equation at the points \( \left(\frac{1}{2}, 0\right) \) and \( \left(\frac{1}{2}, -2\right) \). Convert both tangent line equations to the slope-intercept form \( y = mx + b \).
Transcribed Image Text:Implicitly differentiate the equation \( y^2 + 4xy + x \ln 2x = 0 \). Isolate \( y' \) in the resulting equation. Use the result to find the equations of the tangent lines to the graph of this equation at the points \( \left(\frac{1}{2}, 0\right) \) and \( \left(\frac{1}{2}, -2\right) \). Convert both tangent line equations to the slope-intercept form \( y = mx + b \).
Expert Solution
Step 1

The equation of tangent on the curve f(x,y)= 0, at (a,b) is given by,

(y - b) = y'|(a,b) (x - a) 

Where, y' = dy/dx

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