Find the extreme values of (x, y) = x 2 + 2y 2 subject to the constraint

Find the extreme values of ƒ(x, y) = x² + 2y² subject to the constraint g(x, y) = 4x − 6y = 25.

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(a) Show that the Lagrange equations yield 2x = 42, 4y = -62. (b) Show that if x = 0 or y = 0, then the Lagrange equations give x = y = 0. Since (0,0) does not satisfy the constraint, you may assume that x and y are nonzero. (c) Use the Lagrange equations to show that y = (d) Substitute in the constraint equation to show that there is a unique critical point P.