Use lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x, y) = 2x2y; 2x2 + 4y2 = 12 step 1 we need to optimize f(x, y) = 2x2y subject to the constraint g(x, y) = 2x2 + 4y2 = 12. to find the possible extreme value points, we must use ∇f = λ∇g. we have ∇f = 4xy, $$ correct: your answer is correct. 2x^2 and ∇g = $$ correct: your answer is correct. 4x, $$ correct: your answer is correct. 8y . step 2 ∇f = λ∇g gives us the equations 4xy = 4λx, 2x2 = 8λy. the first equation implies that x = incorrect: your answer is incorrect. or λ = correct: your answer is correct.