5. [-/5 Points] DETAILS LARCALC11M 13.10.005. Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize f(x, y) = x2 + y2 Constraint: x + 2y - 20 = 0 f( eBook 6. [-/5 Points] DETAILS LARCALC11M 13.10.011. Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive. Minimize f(x, y, z) = x2 + y2 + z2 Constraint: x + y + z - 21 = 0 f( eBook7. [15 Points] DETAILS LARCALCH M 1110.033. Use Lagrange multipliers to solve the following exercise. Find three positive integers X, y, and 2 that satisfy the given conditions. The product is 125 and the sum is a minimum. mnzHS) IBM 8. [15 Points] DETAILS LARCALCH M 117.017. (a) Find an equation of the tangent plane to the surface at the given point. x+y+z=14, (5,5,4) S {b} Find a set of symmetric equations for the normal line to the surface at the given point. 0 X 5 = y 5 z 4 5 4 5 OX5=y5=Z4 5 5 4 O=i= 5 5 4 Ox5=y5=z4 05X_=5y=4z . m