Use the method of Lagrange multipliers to find the minimum value of the function f(x, y, z) = x + y + z subject to the constraint x? + y? +z? = 2. Assume no more than two of the variables equal zero, and express the minimum value as an exact answer.

Find the minimum and maximum values of the function f(x, y, z) = 3x + 6y + 4z subject to the constraint x² + 6y² + 14z² = 1. (Use decimal notation. Round your answers to one decimal place.) minimum: maximum:

Find the minimum of the function f(x) = x³ – 5x³ – 13x + 4 using quadratic interpolation. Use x0 = 0, x1 = 2, x2 = 4 as an initial quess. Tip: Make table with x0,x1,x2,x3, f (x0),ƒ (x1), f(x2),f(x3). Remove the worst quess from these and arrange 20,x1,x2 values in ascending order then conducts iteration ie. calculate new x3 and f (x3) iterate again until you get two same į values with for example five decimal points. Insert the numerical value of minium value for f(x) here f_x = -30.176 Verify your answer here fi = -30.176

Find the maximum of v = xyz Subject to the constraint 6x+4y+3z-24=0.