1) If z = f (x, y) is a function that admits second continuous partial derivatives such that ∇f(x, y) = 4x - 4x3 - 4xy2, −4y - 4x2y - 4y3 A critical point of f that generates a relative maximum point corresponds to: A) (0, 1) B) (1, 1)
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1) If z = f (x, y) is a function that admits second continuous partial derivatives such that ∇f(x, y) = 4x - 4x3 - 4xy2, −4y - 4x2y - 4y3
A critical point of f that generates a
A) (0, 1)
B) (1, 1)
C) (0, 0)
D) (−1, 0)
2) Suppose you want to maximize the function V = xy, with positive x, y, subject to the restriction 2x2 + y2 = 3, using the Lagrange multipliers technique. By solving the corresponding system
to this problem the following relationship between the variables is obtained:
A) y = 4λx
B) x = y/√2
C) x = 2λy
D) y = x/√2
3)Consider the equation of the surface S given by In(x2yz3) + xz-x2y = 0
An equation for the plane tangent to S, at the point (1, 1, 1), is given by:
A) 4x + z = −5
B) x + 4z = 5
C) x + 4y = −5
D) y + 4z = 5
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