Question

how to solve
f(x,y) = 4x^3 + y^2 ; 2x^2 + y^2 = 1 using lagrange multipliers????

Answer 1

delf = λdelg
where g = 2x^2 + y^2 -1


(12x^2,2y) =λ(4x,2y)
2y = 2λy
2y(λ-1) = 0
λ = 1,y=0

λ = 1:
12x^2 = 4xλ
4x(λ-3x)=0
4x(1-3x)=0
x = 0, x = 1/3

so for x = 0 plug into 2x^2 + y^2 = 1
y= +/-1
for x = 1/3 plug into 2x^2 + y^2 = 1
y = +/- sqrt(7/9)


y = 0

x = +/- sqrt(2)

Answer 2

thank you so much!!!! ;0)

Answer 3

How would I solve : find the point on the line 2x-4y = 3 that is closest to hte origin using the same method?