Hello,

I need to use the lagrange method to find the extreme values of

$\displaystyle f(y,z)=z^3+yz$

with this condition

$\displaystyle y+3z+24=0$

I got this system of equations

$\displaystyle z-\lambda=0$ (1)

$\displaystyle 3z^2+y-3\lambda=0$ (2)

$\displaystyle y+3z+24=0$ (3)

And I tried to define y in terms of z, $\displaystyle y=3z-3z^2$ and insert in (3)

But I get the wrong answer after solving the new equation.

The right answer is

$\displaystyle (4,-36)$ and $\displaystyle (-2,-18)$

Would anyone mind to explain how to get to the right answer?

Thanks