(Don't worry, this isn't the same question as I posted the other day)

Find the maximum value of

$\displaystyle f(v,w,x,y)=(1,0,6,6)\left( \begin{array}{c} v \\ w \\ x \\ y \end{array} \right)$

subject to the constraint

$\displaystyle v^4+w^4+x^4+y^4=1$

[NB: your answer should be given as a surd, not a decimal.]

To begin with, I multiplied out the function to get

$\displaystyle f(v,w,x,y)=v+6x+6y$

Is that right? If not, can you tell me why? If it is, I then got the following partials...

$\displaystyle \frac{\partial L}{\partial v}=1-4\lambda v^3$

$\displaystyle \frac{\partial L}{\partial w}=-4\lambda w^3$

$\displaystyle \frac{\partial L}{\partial x}=6-4\lambda x^3$

$\displaystyle \frac{\partial L}{\partial y}=6-4\lambda y^3$

$\displaystyle \frac{\partial L}{\partial\lambda}=-(v^4+w^4+x^4+y^4-1)$

...but then rearranging for $\displaystyle v$, $\displaystyle w$, $\displaystyle x$, $\displaystyle y$ and put them into $\displaystyle \frac{\partial L}{\partial\lambda}=0$ I get a really awful expression for $\displaystyle \lambda$ and consequently awful expressions for $\displaystyle v$, $\displaystyle x$ and $\displaystyle y$ (not $\displaystyle w$ 'cause I get that equal to $\displaystyle 0$)

Can anyone maybe see where I've gone wrong? I can tell you what I got for $\displaystyle \lambda$ et cetera if needs be.