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# Classifying multivariable stationary points Watch

1. Please help! Working through old exam papers as revision and really stuck on this question:

Find and classify all stationary points of the following function:

f(x,y)= x^2 + 12xy + 3xy^2 + y^3

I know you have to set the first derivatives to zero and then evaluate D=d^2f/dx^2 . d^2f/dy^2 - (d^2f/dxdy)^2 but I'm not sure how to find the points from the first derivatives? Is this just a huge brain fart and is actually really easy? Lol, any help appreciated
2. (Original post by Vianna)
...
One way:

From df/dx=0 you can re-arrange to get 2x=....

Then sub into df/dy=0, eliminating the x, and simplify.

Where the d's are partial derivatives, of course - just can't be arsed to LaTex it.

It looks horrendous, but it's straight forward to solve for y.
3. (Original post by Vianna)
Please help! Working through old exam papers as revision and really stuck on this question:

Find and classify all stationary points of the following function:

f(x,y)= x^2 + 12xy + 3xy^2 + y^3

I know you have to set the first derivatives to zero and then evaluate D=d^2f/dx^2 . d^2f/dy^2 - (d^2f/dxdy)^2 but I'm not sure how to find the points from the first derivatives? Is this just a huge brain fart and is actually really easy? Lol, any help appreciated
Set the first derivatives to zero
Solve the equation system for (x,y) simultaneously
Subtract df/dx=0 from df/dy=0, arrange to y then substitute this in the df/dx=0 and factorize
You will get 3 solutions
4. (Original post by ghostwalker)
One way:

From df/dx=0 you can re-arrange to get 2x=....

Then sub into df/dy=0, eliminating the x, and simplify.

Where the d's are partial derivatives, of course - just can't be arsed to LaTex it.

It looks horrendous, but it's straight forward to solve for y.
Thanks! All sorted now

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