# Thread: Multi-variable calculus - Stationary points.

1. ## Multi-variable calculus - Stationary points.

I need to find and classify stationary points of:

z = x^2 + 4xy + 4y - 9x + 1

so far I got:

dz/dx = 2x + 4y - 9 and dz/dy = 4x + 4

not sure as to how to go on as Im rubbish at these lol

Thanks

2. ## Re: Stationary points.. HELP!!

Originally Posted by zana
I need to find and classify stationary points of:

z = x^2 + 4xy + 4y - 9x + 1

so far I got:

dz/dx = 2x + 4y - 9 and dz/dy = 4x + 4

not sure as to how to go on as Im rubbish at these lol

Thanks
First you need to solve the system:

dz/dx=0
dz/dy=0

which will give the stationary point/s that you will then need to classify

CB

3. ## Re: Multi-variable calculus - Stationary points.

i know i need to obtain 2 simultaneous equations and substitute x but thats what im stuck on, all i get is x = y which im sure isnt right

4. ## Re: Multi-variable calculus - Stationary points.

Originally Posted by zana
i know i need to obtain 2 simultaneous equations and substitute x but thats what im stuck on, all i get is x = y which im sure isnt right
Your two equations are (we have already told you what they are using your partial derivatives of z):

dz/dx = 2x + 4y - 9=0

and:

dz/dy = 4x + 4=0.

The second of these tells you that for any critical point x=-1, so using the first you find 4y-11=0 or y=11/4.

So now you have the critical point, now you need to determine what type it is.

CB

5. ## Re: Multi-variable calculus - Stationary points.

thank you so much!
calculus is the one bit that gets me.
this is going to sound like a silly question but could you possibly show me how you get x=-1??

6. ## Re: Multi-variable calculus - Stationary points.

Surely you can solve 4x + 4 = 0...

7. ## Re: Multi-variable calculus - Stationary points.

Originally Posted by zana
thank you so much!
calculus is the one bit that gets me.
this is going to sound like a silly question but could you possibly show me how you get x=-1??
I told you that you use the second equation, which was 4x+4=0. Solving this is elementary common algebra and if you are having difficulties with it then you should reconsider your pursuit of calculus before you have reviewed/achieved fluency in algebra.

CB