Pictured below are a contour map of a function f and a curve with equation g(x,

Question

Pictured below are a contour map of a function f and a curve with equation g(x, y) = 8. Estimate the maximum and minimum values of f subject to the constraint g(x, y) = 8. Maximum value is Minimum value is Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 7 x 2 - 4 y 2 on the circle x {2} + y {2} = 9. Maximum value is Minimum value is Use Lagrange multipliers to find the maximum and minimum values of f(x, y, z) = 8 x + 6 y + 8 z on the sphere x {2} + y {2} +z {2} = 41. Maximum value is Minimum value is

Explanation / Answer

1)minimum=30 maximum=60 2)minimum=-36 maximum=63 3)minimum=-82 maximum=82

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