You are Here: Home >< Maths

# Partial differentiation and stationary points Watch

1. Hi all.

I've been asked to find the stationary point of the function u(x,y) = 2x^4 + 8(x^2)y^2 - 4x^2 + 4y^2 .

I know the stationary points lie at the solution of du/dx = du/dy = 0.

So I have found
du/dx = 8x^3 + 16x(y^2) - 8x, and
du/dy = 16(x^2)y + 8y.

Presumable I have to set these 2 equations to =0 and solve simultaneously, but am not sure exactly how to do this. Can anyone advise?

Thanks!
2. That's right. Start by looking at your equation for du/dy. Factorise it and set it equal to zero. You should find that this only works for one value of y. Now take this y value and substitute it into your equation for du/dx. Factorise this and make it equal to zero. You should find three possible x values.
3. Good so far

du/dx=8x^3 + 16x.y^2 - 8x - eqn1
du/dy=16y.x^2+8y - eqn2

check

du/dxdy=32xy
du/dydx=32xy

You put du/dx=0 and du/dy=0 then simplify and you can get values for x and y then put an x value from du/dx into du/dy to find a y-value and vice versa.

eqn1 - 8x^3 + 16x.y^2 - 8x= 0 => 8x(x^2+2y^2-1)=0
eqn2 - 16y.x^2+16y = 0 => 16y(x^2+1)=0
4. Cheers guys, will rep tomorrow. I worked through the rest of the problem and obtained 3 stationary points; a saddle at (0,0) and 2 minima at (1,0) and (-1,0), which I think is the correct answer.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: December 8, 2010
Today on TSR

Find out how.

### Homophobic parents forcing me far away

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.