Answer
-30 , 30
Work Step by Step
f(x,y,z) = x - 2y + 5z
g(x,y,z) = x^{2} + y^{2} + z^{2} - 30
∇f = λ(∇g)
i-2j+5k = lam(2xi + 2yj + 2zk)
1 = 2xλ, -2 = 2yλ , 5 = 2zλ
x = 1/2λ , y = -1/λ , z = 5/2λ
y = -2x , z = 5x
x^{2} + (-2x)^{2} + (5x)^{2} - 30 = 0
x^{2} + 4x^{2} + 25x^{2} = 30
30x^{2} = 30
x = ± 1
y = ∓ 2
z = ± 5
x=1,y=-2,z=5 OR x=-1,y=2,z=-5
f(1,-2,5) = 30 = max value
f(-1,2,-5) = -30 = min value
