Question

Use the Lagrange method to find the constrained ends of the function f(x,y)=x+3y

that are on the curve x²+y²=10

write your answer from the constrained ends of the form f(a,b)=c

If there is no restricted maximum or restricted minimum, write NE

a) Maximum restricted

b) Restricted minimum

Utilice el método de Lagrange para encontrar los extremos restringidos de la función f (2, y) = x + 3y que están sobre la curva z2 + y2 = 10. Escriba su respuesta de los extremos restringidos de la forma f (a, b) = 0 Si no hay máximo restringido o mínimo restringido escriba NE Máximo restringido Mínimo restringido ho

Answer 1

Solution :- Here, fix,y) = x+3y and the cubre is x 2 Let, L(x,y) = x + 3y ta (2 Tyrio) where lagharges multiplier is a. Now, al 10 1 + 2x2 22 - 3+ 2ya DY 21 = a +Y-10 да For stationary points al => sz dy 1+ axa=0 and 3+ Ya so =-1122 3 2a From (2² 3+ ( )= le 1+ 9 =lo 424 42=1 -> az I yd NOW a= -- x = 1 and 7 = 3 and a = + + Ž. x= -1 y = -3 so, fcx,y) | (1,3) : 1 + 3.3 = 1+9 = 10 and = -1 -3.3 = -1-9 = - 10 F(x, y) han maximam aut (13) at (13) and maximum and fix,y) has minimum ent (-1,-3) and minimum value is Name is