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13 Nov 2019
#2 please
Exercises In this exercise set, use the method of Lagrange multipliers unless oth- erwise stated. 1. Find the extreme values of the function f(x, y) = 2x + 4y subject to the constraint g(x, y) = x2 + y2-5-0. (a) Show that the Lagrange equation Vf λâ½g gives λx-1 and (b) Show that these equations imply λ 0 and y = 2x. (c) Use the constraint equation to determine the possible critical points (d) Evaluateãf(x, y) at the critical points and determine the minimum and maximum values. 2. Find the extreme values of,f(x,y)=x2+2y2 subject to the con- straint g (x, y) = 4x-6y = 25. (a) Show that the Lagrange equations yield 2x = 4, 4y =-6A. (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 as- sume that x and y are nonzero. (c) Use the Lagrange equations to show that y =-3x. (d) Substitute in the constraint equation to show that there is a unique critical point P. (e) Does P correspond to a minimum or Figure 13 to justify your answer.Hint: Do the values of f(x, y) increase or decrease as (x, y) moves away from P along the line g (x, y) = 0? 4 maximum value of f? Refer to
#2 please
Exercises In this exercise set, use the method of Lagrange multipliers unless oth- erwise stated. 1. Find the extreme values of the function f(x, y) = 2x + 4y subject to the constraint g(x, y) = x2 + y2-5-0. (a) Show that the Lagrange equation Vf λâ½g gives λx-1 and (b) Show that these equations imply λ 0 and y = 2x. (c) Use the constraint equation to determine the possible critical points (d) Evaluateãf(x, y) at the critical points and determine the minimum and maximum values. 2. Find the extreme values of,f(x,y)=x2+2y2 subject to the con- straint g (x, y) = 4x-6y = 25. (a) Show that the Lagrange equations yield 2x = 4, 4y =-6A. (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 as- sume that x and y are nonzero. (c) Use the Lagrange equations to show that y =-3x. (d) Substitute in the constraint equation to show that there is a unique critical point P. (e) Does P correspond to a minimum or Figure 13 to justify your answer.Hint: Do the values of f(x, y) increase or decrease as (x, y) moves away from P along the line g (x, y) = 0? 4 maximum value of f? Refer to
Elin HesselLv2
5 Sep 2019