You can put the code into the prompt in the MATLAB AI Chat Playground, then ask it to explain it to you.
For example, I asked it to add comments describing the code in terms of the mean value theorem.
clear
clc
syms x y
% Define the function f(x) = x^3 - 12x - 5
f(x) = x^3 - 12*x - 5;
% Specify the interval [a, b] where we will apply the MVT
I = [-4, 4];
a = I(1);
b = I(2);
% Calculate the derivative of the function f
Df = diff(f, x);
% Calculate the slope of the secant line between points (a, f(a)) and (b, f(b))
m = (f(b) - f(a)) / (b - a);
% Solve for c where the derivative equals the slope of the secant line
c = solve(Df == m, x);
% Filter c to find values that lie within the interval [a, b]
c = c(a <= c & c <= b);
% Display the values of c that satisfy the MVT condition
disp('Values of c lying in the interval I are');
disp(double(c));
% Calculate the tangent lines at the points c
T = f(c) + m * (x - c);
% Display the equations of the tangent lines
disp('The Tangent Lines at c are');
disp(vpa(y == T, 4));
% Plot the function f, tangent lines, and secant line for visualization
figure
fplot(f, I);
grid on;
hold on;
% Plot the tangent lines in red
fplot(T, I, 'r');
% Plot the points c on the function in black circles
plot(c, double(f(c)), 'ko');
% Plot the secant line in magenta
plot(I, double(f(I)), 'm');
% Label the axes and title the plot
xlabel('x');
ylabel('y');
title('Demonstration of Lagranges Mean Value Theorem');
