hold on
alpha = 0.3;

x = 0:0.01:1.5;
y = sqrt(x);

h = plot(x, y, 'k');
set(h,'linewidth',2.5); % <- Set linewidth here

L = 1;
% Tangent line
a = 0.5;
x1 = (a-L/2):0.01:(a+L/2);
b1 = sqrt(a);
y1 = (1/2/sqrt(a))*(x1-a) + b1;
h = plot(x1, y1, 'g');
set(h,'linewidth',2); % <- Set linewidth here

h = line([a a], sqrt(a)+[-L/2 L/2]);
set(h,'linewidth',2); % <- Set linewidth here

axis equal
axis off
% MATLAB does not have built-in SVG support. Use the following package to
% convert FIG files to SVG
plot2svg