The language is MATLAB For Q13 use fx 33x3 25x 06 and be

The language is MATLAB

For Q1-3, use f(x) = -3.3x^3 + 2.5x - 0.6, and be sure to modify f.m and f_and_fprime.m accordingly. a) For the interval [0. 0.5], and without using a calculator, prove that f(x) has (i) at least one root using the IVT, and (ii) no more than one root using a sketch of/(x) and Rolle\'s theorem. b) For the other root(s), state a bracketing interval that contains only that one root, and that uses interval end points having a precision of 0.5. c) By evaluating f(X) at x values in increments of 1E-4 within each bracketing interval, find all roots to a precision of 1E-4, and state the number of times f(x) was calculated for each root. function f at x = f(x) f at x = x^3 - exp(-x); end f and fprime function [f at x, fprime at x] = f and fprime(x) f at x = x^3 - exp(-x); fprime at x = 3*x/N2 + exp(-x); end

Solution

%a=0,b=0.5;

%f(a)=-0.6;

%f(b)=+0.2375

%l=0;

% so there exist a root

a = 0;
b = 2.5;
F = \'-3.3*X.^3+2.5*X-0.6\';
h = (b-a)/100;
X = a:h:b;
Y = eval(F);

%X=-ve and y=+ve it means that the graph crosses the x axis min once hence 1 root is there

%for getting all the root

p=[-3.3 0 2.5 -0.6];

r=poly(p);

%r gives all the root