Question

lagrange multiplier:
z = 6x + 6y - 8
find the closest point (x0, y0) to the point (3, -1, -5)

Answer 1

img included

Answer 2

k so you would want to use the distance formula for the (3, -1, -5) point and then plug z into that distance formula to eliminate the z variable

Answer 3

giving \[d ^{2}=(x-3)^{2}+(y+1)^{2}+(6x+6y-3)^{2}\]

Answer 4

now you are supposed to minimize... but how would you go about doing this?

Answer 5

nm i figured it out