Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y) = xy; 14x + y= 16 . . . Find the Lagrange function F(x,y,2). F(x,y,2) = xy -2( 14x+ y-16) Find the partial derivatives Fx, Fy, and Fx. FX = y- 142 Fv = x-2 F1 = - 14x - y+ 16 There is a |maximum value of | located at (x,y) = (Type an integer or a fraction. Type an ordered pair, using integers or fractions.)Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y) = 3x2 + 2y2; 4x + 4y =240 . . . Find the Lagrange function F(x,y,2). F(x,y,2) = 3x2+ 2y2-2(4x + 4y-240) Find the partial derivatives Fx, Fy, and Fx . FX = 6x - 42 Fv = 4y - 42 F1 = -4x - 4y + 240 There is a value of located at (x, y) =. (Type an in pe an ordered pair, using integers or fractions.) maximum minimum6.5 Constrained Optimization: Lagrange Multipliers and the Question 4, 6.5.3 Extreme-Value Theorem Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimu f(x,y) = 2x2 +4y2; 2x+ y = 54 There is a I: value of D located at (x, y) = D. (Simplify your answers.) 6.5 Constrained Optimization: Lagrange Multipliers and the The two numbers whose difference is 52 and that have the minimum product are D. (Simplify your answer. Use a comma to separate answers as needed.) 6.5 Constrained Optimization: Lagrange Multipliers and the The minimum value is E. (Type an integer or a simplied fraction.) 6.5 Constrained Optimization: Lagrange Multipliers and the Question 14, 6.5.44 Extreme-Value Theorem Find the indicated maximum or minimum value of f subject to the given constraint. Maximum: f(x,y,z) = x2y222; x2 + y2 + 22 =10 E) The maximum value is D. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. 6.5 Constrained Optimization: Lagrange Multipliers and the