Register to reply

Implicit differentiation

by aanandpatel
Tags: implicit diff., stationary point
Share this thread:
Feb20-12, 03:55 AM
P: 16
1. The problem statement, all variables and given/known data

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

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

3. 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 :)
Phys.Org News Partner Science news on
Hoverbike drone project for air transport takes off
Earlier Stone Age artifacts found in Northern Cape of South Africa
Study reveals new characteristics of complex oxide surfaces
Feb20-12, 04:36 AM
HW Helper
P: 10,350
Hi aanandpatel,

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

Feb20-12, 06:43 AM
Sci Advisor
PF Gold
P: 39,310
You have two equations,
[tex]x^3 + (3x^2)(y) -2y^3=16[/tex]
[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.

Feb21-12, 04:37 AM
P: 16
Implicit differentiation

Thanks guys - helped a lot! :)

Register to reply

Related Discussions
Implicit differentiation help Calculus & Beyond Homework 3
Implicit differentiation Calculus & Beyond Homework 2
Solve by Implicit Differentiation or Partial Differentiation? Calculus & Beyond Homework 12
Implicit differentiation Calculus & Beyond Homework 2
Implicit differentiation Calculus & Beyond Homework 3