Question

Lagrange:

f(x,y) = x^2*y^2

9x^2+4y^2 = 36

Find local max and min

Answer 1

could you explain the answer?

Answer 2

g(x) = 9x^2 + 4y^2 - 36

so del(f) = λdel(g)

delf = 2x*y^2i + 2y*x^2j

delg = 18xi + 8yj

2xy^2 = λ18x
2yx^2 = λ8y

y^2 =9 λ
x^2 = 4λ

9*4λ + 4*9λ - 36 = 0
72λ = 36
λ = 1/2

y^2 = 4.5
x^2 = 2

y = +/- sqrt(4.5)
x = +/- sqrt(2)

Answer 3

CoolSector Saves the Day!

Answer 4

hope im right lol

Answer 5

hee yeahh o.o

but what about the local min and maX?

Answer 6

oh you have to plug the values and see which is bigger

Answer 7

but the minus roots doesnt count right?

so its just, ( sqrt(4,5) , sqrt(2) )?

Answer 8

i think they will all have the same value
so just pick another point
and see if it is bigger or smaller

Answer 9

i need the second derivative and see if fxx is > 0 of < 0

Answer 10

thank yoouu soo much coolsector <3

Answer 11

youre welcome. i hope it is correct :)