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Use Lagrange multipliers to find the maximum and minimum values of?
Use Lagrange multipliers to find the maximum and minimum values of f(x, y, z) = 3x + 3y + 5z on the sphere x^2 + y^2 + z^2 = 1.
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- δοτζοLv 77 years ago
<3,3,5> = λ<2x,2y,2z>
x²+y²+z²=1
3/2 = λx
3/2 = λy
5/2 = λz
(9/4) + (9/4) + (25/4) = 43/4 = λ² ⇒ λ = ±√43 / 2
Plug those into the above and you'll get your maximum and minimum.
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