How do I get the minimum/maximum of one of the graphs I have plotted?

a=[.2:.01:1];
E_A=(-1.436)./a;
E_R=(5.86*10.^(-6))./(a.^9);
E_N=E_A+E_R; % <<<<<<----- I am trying to find the min of this equation but i cant figure out how to
plot(a,E_A);
hold on
plot(a,E_R);
plot(a,E_N);
title('Energy vs. Distance between atoms')
ylabel('Energy (eV)')
xlabel('Distance between atoms (nm)')
legend('E_A','E_R','E_N')

Answer 1

[Walter Roberson]

[min_E_N, min_pos] = min(E_N);
[max_E_N, max_pos] = max(E_N);
a_at_min = a(min_pos);
a_at_max = a(max_pos);
plot(a_at_min, min_E_N, 'rv', a_at_max, max_E_N, 'g^')

[Dakota Fike]

That was quick! Thank you so much Mr.Roberson!

[Dakota Fike]

I do have a couple of questions though what is min_pos, when I display that information it shows that it equals 9? I was also wondering If you knew how to display the x and y coordinates of this position, pointing to it, similar to the image shown below?

<<

>>

[Walter Roberson]

min_pos is the index within E_N at which the minimum occurs. When you give only E_N, MATLAB cannot know which a generated that particular value, but it can know the relative position the minimum was found in, and then you can use that relative position to look up the associated a value.

For creating the data tips, I adapt code from https://undocumentedmatlab.com/blog/controlling-plot-data-tips

a=[.2:.01:1];
E_A=(-1.436)./a;
E_R=(5.86*10.^(-6))./(a.^9);
E_N=E_A+E_R; % <<<<<<----- I am trying to find the min of this equation but i cant figure out how to
plot(a,E_A);
hold on
E_r_line = plot(a,E_R);
E_N_line = plot(a,E_N);
title('Energy vs. Distance between atoms')
ylabel('Energy (eV)')
xlabel('Distance between atoms (nm)')
legend('E_A','E_R','E_N')

[min_E_N, min_pos] = min(E_N);
[max_E_N, max_pos] = max(E_N);
a_at_min = a(min_pos);
a_at_max = a(max_pos);

cursorMode = datacursormode(gcf);
datatip(1) = cursorMode.createDatatip(E_N_line);
datatip(2) = cursorMode.createDatatip(E_N_line);
datatip(1).Position = [a_at_min, min_E_N, 0];
datatip(2).Position = [a_at_max, max_E_N, 0];