Find x-Coordinates of Points on y=3x/(2x-3) with Normal Parallel to 9y=4x+3

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Homework Help Overview

The discussion revolves around finding the x-coordinates of points on the curve defined by the equation y=3x/(2x-3) where the normal line is parallel to a given line represented by the equation 9y=4x+3. Participants are exploring the relationship between the slopes of the normal line and the tangent line to the curve.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need to find the derivative of the curve and the slopes involved. There are questions about the slopes of the given line and its normal, as well as how to set the derivative equal to the slope of the normal line.

Discussion Status

Some participants have offered guidance on finding the derivative and understanding the slopes involved. There is an ongoing exploration of the relationships between the slopes and the points on the curve, with no explicit consensus reached yet.

Contextual Notes

Participants are working under the constraints of homework guidelines, which may limit the extent of assistance provided. There is a mention of a potential coincidence in the problem being discussed, indicating that multiple participants are engaging with similar content.

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Find the x-coordinates of the points on the curve [tex]y=\frac{3x}{2x-3}[/tex] where the normal is parallel to the line 9y=4x+3.

Could someone tell me what to do?
 
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Ask Omicron,apparently he's found a way to solve the same problem.

Daniel.

P.S.My advice would normally include find the derivative,the equation of the normal and then put the condition of parallelism and find the "x" intercept.
 
Yes, apparently I found a way.
Find the derivative
Gradient of 9y=4x+3 and normal => 4/9
Gradient of the tangent line => -9/4
Set -9/4 = derivative

You know, its too coincidental that you got the same question as me? :rolleyes:
 
Last edited:
1. What is the slope of the line 9y= 4x+ 3?

2. What is the slope of a line normal to that?

3. At what points is the derivative of y(x) equal to the answer you got to 2?
 

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