Given the function : f(x) = x³ + 5x² + 7x − 20; solve using Bisection Method with initial values of (1.000, 2.000) 1st iteration xn = 1.000 xp = 2.000 xnew = 1.500 2nd iteration xn = 1.000 xp = 1.500 xnew = 1.250 3rd iteration xn = 1.250 xp = 1.500 xnew = 1.375 4th iteration xn = 1.250 xp = 1.375 xnew = 1.312 5th iteration xn = 1.250 xp = 1.312 xnew = 1.281 f(xn) = -7.000 f(xp) = 22.000 f(xnew) = 5.125 f(x) = -7.000 f(xp) = 5.125 f(xnew) = -1.484 f(xn) = -1.484 f(xp) = 5.125 f(xnew) = 1.678 f(xn) = -1.484 f(xp) = 1.676 f(xnew) = 0.049 f(x) = -1.484 f(xp) = 0.049 f(xnew) = -0.726

Given the function : f(x) = x³ + 5x² + 7x-20; solve using Secant Method with initial values of (1.000, 2.000) 1st iteration X0 = 1.000 X1 2.000 xnew = 1.241 2nd iteration X0 = 2.000 X1 2.000 xnew 1.296 3rd iteration X0 = 1.241 X1 = 1.296 xnew= 1.310 4th iteration X0 = 1.296 X1 = 1.310 xnew= 1.310 5th iteration X0 = -0.001 X1 = -0.001 xnew= 1.310 f(x0) = -7.000 f(x1) = 22.000 f(xnew) = -1.701 f(x0) = 22.000 f(x1) = -1.701 f(xnew) = -0.353 f(x0) = -1.701 f(x1) = -0.353 f(xnew) -0.001 = f(x0) = -0.001 f(x1) = -0.001 f(xnew) = -0.001 f(x0) = 1.310 f(x1) = -0.001 f(xnew) = -0.001

Paul's firm produces the same good as Sal's firm. The total cost of producing qp units in Paul's firm is Cp( qp ) = 8.6 qp + 1.1. The total cost of producing qs units in Sal's firm is    Cs( qs ) = 8.6 qs + 1.1. What is the efficiency loss if each person's firm produces half of a total of 523 units?

The yield in bushels from a grove of orange trees is given by Y = x(1000 − x), where x is the number of orange trees per acre. How many trees will maximize the yield?