software of programming, graphing numerical derivative

hw9.m

clear
clc

hold('on');
x = 0:0.01:5;
y = x.^2;
p = plot(x, y, 'LineWidth', 2, 'Color', [.2, .5, 1]);
axis([0, 5, 0, 25])

tangent = 2*x-1;
t = plot(x, tangent, 'LineWidth', 2, 'Color', [0.9, .54, .3]);

% l1 = plot([1 ; 1 ],[0 ; 0 ],  'LineWidth', 1, 'Color', 'r');
[m, yidx] = min(abs(x-1)) % grab the index where x = 1
l2 = plot([1 x(end) 1; 1 x(end) x(end) ], [0 0 y(yidx); y(yidx) y(end) y(end)],  'LineWidth', 1, 'Color', 'r');
s = size(x);
s = s(end); % get the size of the array, use that to determine x values to use when creating the animation.

% add text to match the assignment video
x1 = 0.5;
y1 = 15;
txt1 = 'lim f(1+h)/h as h->0 approaches';
text(x1,y1,txt1);
txt2 = 'the slope of the tangent line which is';
text(x1,y1-1,txt2);
txt3 = 'equal to the derivativeat that point.';
text(x1,y1-2,txt3);

x2 = 3.4;
y2 = 10;
text(x2, y2, 'f(x) = x^2');
text(3, 3, 'tangent line: t(x) = 2x-1');
text(3, 2, 'slope: df/dx(1) = 2');

for i = s:-3:(yidx+1) % modify middle value to change step size/speed

    % g'ddam it matlab, why
    x1 = [1 x(i) 1];
    x2 = [ 1 x(i) x(i)];
    y1 = [0 0 y(yidx)];
    y2 = [y(yidx) y(i) y(i)];
    for ii = 1:numel(l2) 
        l2(ii).XData = [x1(ii) x2(ii)];
        l2(ii).YData = [y1(ii) y2(ii)];
    end
%     set(l2,'XData',[1 x(i) 1; 1 x(i) x(i) ], 'YData',[0 0 y(yidx); y(yidx) y(i) y(i)]);

    title(['slope = ', int2str((y2(end) - y1(end))/(x2(end) - x1(end)))])
    drawnow()
end