% Problem # 13 (or Fichtenholz's Function # 3)
% Range of initial points: 0.001 <= x <= 0.99
% Global maxima: x=1/sqrt(2)
% f(x)=1.587401051968199
% Coded by: Ali R. Alroomi | Last Update: 25 Feb. 2015 | www.al-roomi.org
 
clear
clc
warning off
 
xmin=0.001;
xmax=0.99;
R=100000; % steps resolution
x=xmin:(xmax-xmin)/R:xmax;
 
for i=1:length(x)
    f(i)=x(i)^(2/3)+(1-x(i)^2)^(1/3);
end
 
plot(x,f,'r','LineWidth',2);grid;set(gca,'FontSize',12);
xlabel('x','FontName','Times','FontSize',20,'FontAngle','italic');
ylabel('f(x)','FontName','Times','FontSize',20,'FontAngle','italic');