Question

4. Given (x)=x-5x + 5x5x2 - 6x , write a symbolic MATLAB script that: (a) plots g(x) in the interval -2 <x< 4, (b) finds and display all of its maxima and minima, (c) evaluates g(x) at the following values of x: -21, 21, 0, 1, 2st and displays the five results. tidad

Answer 1

MATLAB CODE:

clc
clear all
close all

syms x

g(x) = x^5 - 5*x^4 + 5*x^3 + 5*x^2 - 6*x;   % Given g(x)

Dg(x) = diff(g(x),x) == 0;    % Differentiation of g(x)
x_data = vpa(solve(Dg(x),x)); % x-values at which maxima and minima exist

g_data = g(x_data);   % Maxima and Minima of g(x)

fprintf('Maxima and Minima of g(x):\n\n')
disp(g_data)

fplot(x,g(x),[-2 4])
xlabel('x')
ylabel('g(x)')
title('Plot of g(x) in the interval -2 < x < 4')
grid on

x = [-2*pi;pi;0;pi;2*pi];
g = vpa(g(x));

fprintf('The 5 values of g(x) are:\n\n')
disp(g)

OUTPUT:

Plot of g(x) in the interval-2 <x< 4 100 g(x) -100 NE w

Maxima and Minima of g(x): -1.4186966255829238763011422249427 1.4186966255829238763011422249427 3.6314322084488407950169898612664 -3.6314322084488407950169898612664 The 5 values of g(x) are: - 18590.517063196329599103759598574 4.5040791006764016213178166351208 4.5040791006764016213178166351208 3399.8466737995139860266860083758