EXPERIMENT 1-B
1. Find the local and global maxima and minima for the function
x3
-12x-5, x
∈
(-4,4).
Solution:
The following MATLAB code illustrates the evaluation and visualization of global and local extrema of a
function f (x) in an interval (a, b).
clear all
clc
syms x
f = input ('Enter the function f(x):');
I = input ('Enter the interval: ');
a=I (1); b=I (2);
df = diff (f, x);
ddf = diff (df, x); f = inline(vectorize(f));
df = inline(vectorize(df));
ddf = inline(vectorize(ddf));
range = linspace (a, b,100);
plot (range, f(range),'-b','LineWidth',2);
legstr = {'Function Plot'}; % Legend String
hold on;
guesses = linspace (a, b,5);
root = zeros(size(guesses));
for i=1: numel(guesses)
root(i) = fzero (df, guesses(i));
end
root = root (a <= root & root <=b);
root = unique(round(root,4));
plot (root, f(root),'ro','MarkerSize',10);
legstr = [legstr, {'Critical Points'}];
disp (['Critical Points of f(x) are: ', num2str(root)])
maxp = root(ddf(root) < 0);
if(numel(maxp) ~= 0)
disp (['Local maximum of f(x) occurs at: ', num2str(maxp)])
end
minp = root(ddf(root) > 0);
if(numel(minp) ~= 0)
disp (['Local minimum of f(x) occurs at: ', num2str(minp)])
end
fval = f(root);
if(numel(maxp) ~= 0)
gmax = root (fval == max(fval));
disp (['Global maximum of f(x) occurs at: ', num2str(gmax),' and its value is:',
num2str(max(fval))]) plot (gmax, f(gmax),'m+','MarkerSize',10);
legstr = [legstr, {'Global Maximum'}];
end
if(numel(minp) ~= 0)
gmin = root (fval == min(fval));
disp (['Global minimum of f(x) occurs at: ', num2str(gmin),' and its value is: ',
num2str(min(fval))]) plot (gmin, f(gmin),'m*','MarkerSize',10);
legstr = [legstr, {'Global Minimum'}];
end
legend (legstr, 'Location', 'Best')
Input : Enter the function f(x): x^3-12x-5
