clearvars
format long
disp('Solution to exercise problem');
fprintf('%s\n','Demonstration of tangents at a point');

% fprintf('%s\n','for the equation y=f(x)=x^2');
% f1=inline('x^2');
% str0=('Plot of y=f(x)=x^2');

% fprintf('%s\n','for the equation y=f(x)=10x');
% f1=inline('10*x');
% str0=('Plot of y=f(x)=10x');

% fprintf('%s\n','for the equation y=f(x)=1');
% f1=inline('1');
% str0=('Plot of y=f(x)=1');

% fprintf('%s\n','for the equation y=f(x)=x^2+x+1');
% f1=inline('x^2+x+1');
% str0=('Plot of y=f(x)=x^2+x+1');

fprintf('%s\n','for the equation y=f(x)=x^3-5x^2+6x+3');
f1=inline('x^3-5*x^2+6*x+3');
str0=('Plot of y=f(x)=x^3-5x^2+6x+3');

fprintf('%s\n\n','where slope m (at point a) = ( f(a+h) - f(a) ) / h');


x_value = input('At what point a is tangent desired (enter value from 0 to 12)?');
h=1;
smallest_h=1/2048;
while h>smallest_h
    slope=( f1(x_value+h)-f1(x_value) ) / h;
    fprintf('for h=%f : then ( f(%f+%f)-f(%f) )/ %f) = ( %f-%f)/ %f) = %f\n',...
                 h,x_value,h,x_value,h,f1(x_value+h),f1(x_value),h,slope);
    h=h/2;
end   

grid on
xlabel('x coordinate','FontSize',10,'Color','k')
ylabel('y coordinate','FontSize',10,'Color','b')
set(gca,'YLim',[0 100],'YTick',0:5:100,'YGrid','on')
set(gca,'XLim',[0 10],'XTick',0:1:10,'XGrid','on')
hold on
% axis equal;
% quiver(0,0,3,0,'g','LineWidth',1.5);
% quiver(0,0,0,3,'g','LineWidth',1.5);
X1=0:.05:12;
imax=length(X1);
% X2=X1.^2;
% X2=10*X1;
% X2=X1./X1;
% X2=X1.^2+X1+1;
X2=X1.^3-5*X1.^2+6*X1+3;
plot(X1,X2,'-r','LineWidth',2)


str1=(''); str2=(''); str3=('');
% str3=sprintf('singular value of A=%f',s(1));
str=sprintf('%s\n',str0);
% str=sprintf('%s\n %s\n %s\n %s\n',str0, str1, str2, str3);
title(str);                        %print title with line breaks
%print -djpeg lesson1_exercise5.jpg;