# Math Help - Lagrange Multiplier

1. ## Lagrange Multiplier

See attach for the question. My answer is incorrect. Where did I go wrong?

$V = x^2y = 900$

$SA = 6xy$

$f_x = 6y$

$f_y = 6x$

$g_x = 2xy$

$g_y = x^2$

$6x = 2xy \lambda$

$6x = x^2 \lambda$

$\frac{3x}{xy} = \frac{6x}{x^2}$

$3x^3 = 6x^2y$

$\frac{1}{2}x = y$

$x^2 (\frac{1}{2}x) = 900$

$x = 12.1644$

$y = 6.0822$

2. Originally Posted by Macleef
See attach for the question. My answer is incorrect. Where did I go wrong?

$V = x^2y = 900$

$SA = 6xy$

$f_x = 6y$

$f_y = 6x$

$g_x = 2xy$

$g_y = x^2$

$6x = 2xy \lambda$ (**)

$6x = x^2 \lambda$

$\frac{3x}{xy} = \frac{6x}{x^2}$

$3x^3 = 6x^2y$

$\frac{1}{2}x = y$

$x^2 (\frac{1}{2}x) = 900$

$x = 12.1644$

$y = 6.0822$
I believe here (**)