## anonymous 5 years ago solve max and min f(x,y) = 2xy subject to x^2 +y^2 = 18

1. anonymous

Use polar coordinates. so x=rcos(theta) y=rsin(theta). So you get r=3root3. now f(x,y)=f(rcostheta,rsintheta)=2r^2sinthetacostheta. We know that r=3root3. So plug in r in f(x,y), so then f(rcostheta,rsintheta)=2(9)(3)(sin)(cos). Now take a partial derivative with respect to thetha and set it equal to 0. and solve for theta

2. anonymous

oh I thought we use Lagrange multipliers$\lambda$

3. anonymous

Oh lagrange multipliers also work!