Question

solve max and min
f(x,y) = 2xy subject to x^2 +y^2 = 18

Answer 1

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

Answer 2

oh I thought we use Lagrange multipliers\[\lambda\]

Answer 3

Oh lagrange multipliers also work!