Implicit Differentiation and coordinates

Click For Summary

Homework Help Overview

The problem involves implicit differentiation and finding coordinates of a point on a curve defined by the equation x³ - xy + y³ = 0. The goal is to determine the point in the first quadrant where the tangent line to the curve is parallel to the x-axis.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to solve for one variable in terms of the other using the derived derivative equation. There is a focus on ensuring that the solutions satisfy both the derivative condition and the original curve equation.

Discussion Status

Some participants have provided guidance on how to approach solving the system of equations derived from the conditions set by the problem. Multiple interpretations of the equations are being explored, but there is no explicit consensus on a single method or solution path.

Contextual Notes

Participants note that the problem involves two equations with two unknowns, emphasizing the need to satisfy both the derivative condition and the original curve equation simultaneously.

Kar91102
Messages
1
Reaction score
0

Homework Statement


Find the coordinates of the point in the first quadrant at which the tangent line to the curve x3-xy+y3=0 is parallel to the x-axis.

SO:
x= +
y= +
mtan=0

Homework Equations



[tex]\frac{dy}{dx}=m_{tan}[/tex]

The Attempt at a Solution



[tex]\frac{dy}{dx}=\frac{y-3x^{2}}{3y^{2}-x}=0[/tex]

After I get the derivative, I have no clue what to do.
 
Physics news on Phys.org
you have two equations two variables so solve for one of the variables
 
For the derivative to equal zero x and y must satisfy y-3x^2=0, right? But x and y must also be on the curve so x^3-xy+y^3=0. That's two equations in two unknowns. Solve them.
 
You now have two equations to solve for x and y. Oh, and here's a simplification:
a fraction is 0 only when its numerator is 0.

Blast! I walked away from the computer and Dick got in ahead of me!
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 15 ·
Replies
15
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 25 ·
Replies
25
Views
2K
  • · Replies 24 ·
Replies
24
Views
2K
Replies
4
Views
3K
Replies
3
Views
2K
  • · Replies 32 ·
2
Replies
32
Views
4K
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K