(a)
%%% Matlab code
clc;
close all;
clear all;
format long
syms x;
f=x^4-3*x^2+x;
a=-1.5;
b=1.5;
figure;
ezplot(f,[a,b]);
grid on;
xlabel('x');
ylabel('f(x)');
df=diff(f,x);
figure
ezplot(df,[a,b]);
grid on
xlabel('x');
ylabel('f''(x)');
disp(' 3 critical point available');
c1=vpasolve(df,x,[-1.5 -1]);
c2=vpasolve(df,x,[-1 0.6]);
c3=vpasolve(df,x,[0.6 1.5]);
f1=[subs(f,a) subs(f,c1) subs(f,c2) subs(f,c3) subs(f,b) ];
fmax=max(f1);
fmin=min(f1);
fprintf('Maximum of function fmax= %f \n',fmax);
fprintf('Minimum of function fmin= %f \n',fmin);
OUTPUT:
3 critical point available
Maximum of function fmax= 0.084135
Minimum of function fmin= -3.513905
(b)
%% Matlab code %%%
clc;
close all;
clear all;
format long
syms x;
f=x^3/4-sin(x)+1/2;
a=0;
b=2*pi;
figure;
ezplot(f,[a,b]);
grid on;
xlabel('x');
ylabel('f(x)');
df=diff(f,x);
figure
ezplot(df,[a,b]);
grid on
xlabel('x');
ylabel('diff(f(x))');
disp(' only 1 critical point available');
c1=vpasolve(df,x,[0 2]);
f1=[subs(f,a) subs(f,c1) subs(f,b) ];
fmax=max(f1);
fmin=min(f1);
fprintf('Maximum of function fmax= %f \n',fmax);
fprintf('Minimum of function fmin= %f \n',fmin);
OUTPUT:
only 1 critical point available
Maximum of function fmax= 62.512553
Minimum of function fmin= -0.101123
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