


iu [5 marks]b ii)) Consider the function, f, as the followings,vRuǐ (x1, x2)-5xỈ + x-. + 4x1 x2-14x1-6x2 + 20 ( !0% x») This function has its optimal solution atx"= (1,1) and f(1, 1) 10. Run t...
(a) Given the following function f(x) below. Sketch the graph of the following function A1. f () 3 1, 12 5 marks (b) Verify from the graph that the interval endpoints at zo and zi have opposite signs. Use the bisection method to estimate the root (to 4 decimal places) of the equation 5 marks] (c) Use the secant method to estimate the root (to 4 decimal places) of the equation 6 marks that lies between the endpoints given. (Perform...
Consider the function f(x) := v/x= x1/2. 6. (a) Give the Taylor polynomial P(x) of degree 5 about a1 of this function (b) Give the nested representation of the polynomial Qs()Ps((t)) where t -1 ((t)+1). (c) Using the nested multiplication method (also called Horner's algorithm), compute the approximation Ps (1.2) to V (give at least 12 significant digits of P(1.2)) (d) Without using the exact value of 12, compute by hand an upper bound on the absolute error V1.2 A(1.21...
1) (80pts) Consider the following function f(x)--x5-4x4 + 2x3 + x2-3x + 5 Develop a simple program which will give an iterative solution to the problem f(x)=0 by Newton's algorithm. The solution should display the results on an Excel spreadsheet such as the one given below (the example below is given for a different function). Choose the programming language which suits you most, however the program should be able to read data from an Excel spreadsheet and write the successive...