Originally Posted by

**Macleef** Use the method of Lagrange multipliers to find the min value of:

$\displaystyle f(x, y) = 5x^2 - 4x^2$ subject to the constraint $\displaystyle g(x, y) = x^2 + y^2 = 9$

Here's what I have so far:

$\displaystyle f_x = 10x$

$\displaystyle f_y = -8y$

$\displaystyle g_x = 2x$

$\displaystyle g_y = 2y$

$\displaystyle 10x = 2 \lambda x$ (**)

$\displaystyle -8y = 2 \lambda y$

$\displaystyle 9 = x^2 + y^2$

$\displaystyle \frac{5x}{x} = \lambda$

$\displaystyle -\frac{4y}{y} = \lambda$

$\displaystyle \frac{5x}{x} = -\frac{4y}{y}$

$\displaystyle 5xy = -4xy$

and now... I don't know how to isolate for x or y.