Find all vertical tangent lines of a curve - more than one variable

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SUMMARY

The discussion focuses on finding vertical tangent lines for the curve defined by the equation xy² - x³y = 6. The derivative of the curve is given as (3x²y - y²) / (2xy - x³). Participants conclude that vertical tangent lines occur when the denominator of the derivative, 2xy - x³, equals zero, indicating points where the derivative is undefined. The need for implicit differentiation is emphasized to correctly derive the derivative and identify vertical tangents.

PREREQUISITES
  • Understanding of implicit differentiation
  • Familiarity with calculus concepts, specifically derivatives
  • Knowledge of polynomial equations
  • Ability to solve equations involving multiple variables
NEXT STEPS
  • Study implicit differentiation techniques in calculus
  • Practice solving polynomial equations with multiple variables
  • Learn how to identify vertical and horizontal tangents in curves
  • Explore the application of derivatives in analyzing curve behavior
USEFUL FOR

Students studying calculus, particularly those focusing on multivariable functions and derivatives, as well as educators teaching implicit differentiation and curve analysis.

mwilks
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find all vertical tangent lines of a curve - more than one variable!

curve : xy^2 - x^3y = 6
derivative : (3x^2y - y^2) / (2xy - x^3)
question : find the x coordinate of each point on the curve where the tangent line is vertical.

after some consideration, i decided that when the derivative equation is underfined, the tangent line is vertical. so, 2xy-x^3=0. was that right? now what?
 
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How did you arrive at that "derivative"?
 


Look up implicit differentiation in your course book. Seems you tried to do it but made some error on the way. Try showing your steps to us.
 

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