can anyone explain the code my calculus teacher explained this code in my class but I didn't understand it. The code is related to Mean value theorem.

clear

clc

syms x y

f(x)=x^3-12*x-5;I=[-4,4]; % Input the function and interval

a=I(1);b=I(2);

Df=diff(f,x);

m=(f(b)-f(a))/(b-a); %Slope of Secant Line

c=solve(Df==m, x);

c=c(a<=c&c<=b);

disp('Values of c lying in the interval I are');

disp(double(c));

T=f(c)+m*(x-c); %Tangents at x=c

disp('The Tangent Lines at c are');

disp(vpa(y==T,4));

figure

fplot(f,I); grid on; hold on;

fplot(T, I, 'r'); %Tangent Lines

plot(c, double(f(c)), 'ko');

plot(I, double(f(I)), 'm'); %Secant Line

xlabel('x'); ylabel('y');

title('Demonstration of Lagranges Mean value theorem');

Answer 1

[Cris LaPierre]

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');