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The tangent line to the graph of y = ln(2x) is perpendicular to a + 4y = 1 at the point where :Select one x = 2 .a x = } b %D x = 4.c

The tangent line to the graph of y = ln(2x) is perpendicular to a + 4y = 1 at the point where :Select one x = 2 .a x = } b %D x = 4.c

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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The tangent line to the graph of y = ln(2x) is perpendicular to a + 4y = 1 at the point where :Select one x = 2 .a x = } b %D x = 4.c
Transcribed Image Text:The tangent line to the graph of y = ln(2x) is perpendicular to a + 4y = 1 at the point where :Select one x = 2 .a x = } b %D x = 4.c
Expert Solution
Step 1

Given,

The tangent line to the graph of y=ln(2x) is perpendicular to x+4y=1

Here,

y=ln(2x)

To find the slope,

Differentiate the above equation with respect to x we get,

dydxln2x=12xddx(2x)ddx(2x)=2⇒12x(2)⇒1x

Step 2

⇒m1=1x

Now for finding the slope for the line x+4y=1

Differentiate the above line with respect to the x we get,

ddxx+4y-1⇒1+4ddx(y)=0⇒ddx(y)=-14⇒m2=-14

Here the tangent line is perpendicular to the line x+4y=1

So, the product of slope is -1

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