Implicit differentiation

  • #1

Homework Statement



Find the coordinates of the stationary points on the curve:
x^3 + (3x^2)(y) -2y^3=16


Homework Equations


Stationary points occur when the first derivative of y with respect to x is equal to zero



The Attempt at a Solution


I implicitly differentiated the equation and got
dy/dx = (x^2 + 2xy) / (2y^2 - x^2)

I know I have to make this equal to zero but then I'm not sure how to find the x and y coordinates of the stationary point.

Help would be greatly appreciated :)
 

Answers and Replies

  • #2
ehild
Homework Helper
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Hi aanandpatel,

Find y in terms of x from the condition dy/dx=0. Substitute back into the original equation.

ehild
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,847
964
You have two equations,
[tex]x^3 + (3x^2)(y) -2y^3=16[/tex]
and
[tex](x^2 + 2xy) / (2y^2 - x^2)= 0[/tex]
to solve for x and y. The second equation can easily be solved for y in terms of x since a fraction is equal to 0 if and only if the numerator is 0.
 
  • #4
Thanks guys - helped a lot! :)
 

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