Question

5. Consider the following first order system: (a) Find the equilibrium point (s). (b) Obtain linear functions that approximate the system for each equilibrium point. (c) Use Matlab to plot the original function(+22 -2) and the linear approx- imations all on the same plot. For the x axis limits on the plot use -2.5 to 2.5

Answer 1

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 Answer(c) Type the following code in matlab to plot all functions
clc
clear all

x=-2.5:0.1:2.5;

fx=x.^3+x.^2-(2.*x);
 plot(x,fx)

ylabel('function outputs');

xlabel('x axix or input');

xlim([-2.5 2.5])

hold on

fx1=-2.*x;
 plot(x,fx1)

hold on
 fx2=(3.*x)-3;
 plot(x,fx2)

hold on
 fx3=(6.*x)+12;
 plot(x,fx3)

grid on

title('effect of linearzing function at different equilibrium point')

legend('original f(x)=x^3+x^2-2x','f(x1)=-2x','f(x2)=3x-3','f(x3)=6x+12')

REsult

original f(x)FX +x -2x f(x1)-2x f(x2)F3x--3 f(x3) 6x+12