Question

please show answer in full with explanation, also show matlab

1. Consider the function f(x)2.753 +18r2 21 12 a) Plot the graph of f(x) in MATLAB and find all the roots of the function f(x) graphically. Provide the code and the plot you obtained. b) Compute by hand the first root of the function with the bisection method, on the interval -1; 0) for a stopping criterion of 1% c) How many iterations on the interval -1, 0 are needed with the bisection method to obtain the true error of the first root less than 10-8 d) Find al the roots applying MATLAB's built-in procedure. Include the MATLAB code used and the output obtained.

Answer 1

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AS FOR GIVEN DATA.

Matlab Code

clc clear all close all % ******* Part a *********** % %--------------------------- % % defining the function f = @(x) -2.75*x.^3 + 18*x.^2 - 21*x - 12; % plotting the function fplot(f, [-2 5]) title(['Graph of the function f(x) = ', char(f)]) % ******* Part b *********** % %--------------------------- % % solving with bisection method err = 10^-8; a = -1; b = 0; root = (a+b)/2; iter = 0; while (abs( (a - b) / root)) > err    if f(root) > 0 a = root; else b = root; end    root = (a+b)/2; iter = iter + 1; end fprintf('Root by bisection method = %.12f\n', root) % Part c % fprintf('Number of iterations taken to find the root by bisection method = %d\n', iter) % ******** part d ************* % ---------------------------- % % defining the coefficients of the equation p = [-2.75 18 -21 -12]; % finding roots using inbuilt function roots_by_inbuiltFunction = roots(p)

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