3) 4) 5) 6) Find the absolute maximum and absolute minimum values of 2X + 3y...

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3) 4) 5) 6) Find the absolute maximum and absolute minimum values of 2X² + 3y² - 4x - 5 on the region X² + y² ≤ 25. Show that the surfaces 3X² + 2Y² + Z² = 9 and x² + y² + Z² 8X - 6Y - 8Z + 24 0 have a common tangent plane at the point (1, 1, 2) = Find the maximum and minimum values that 3x - y attains on the intersection of the surfaces x + and x² + 2z² = 1. Find, using Lagrange multiplier(s), the shortest distance from the point (2, 0, -3) to the plane X + Y + Z = 1 3) 4) 5) 6) Find the absolute maximum and absolute minimum values of 2X² + 3y² - 4x - 5 on the region X² + y² ≤ 25. Show that the surfaces 3X² + 2Y² + Z² = 9 and x² + y² + Z² 8X - 6Y - 8Z + 24 0 have a common tangent plane at the point (1, 1, 2) = Find the maximum and minimum values that 3x - y attains on the intersection of the surfaces x + and x² + 2z² = 1. Find, using Lagrange multiplier(s), the shortest distance from the point (2, 0, -3) to the plane X + Y + Z = 1

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