Stationary point, local minimum, local maximum and inflection point

I am given some function of x1 and x2. Example f(x1,x2)=3x1^2+2x1x2+2x2^2+7. How can I find the stationary point, local minimum, local maximum and inflection point from that function using matlab? Please tell me the feature that can be used and the coding, because I am really new in this field. Thank you in advance.

[reman]

syms x y

% Define the function f(x,y)

f = 8*x^2 + 6*y^2 - 2*y^3 + 5;

% Compute the partial derivatives of f(x,y) with respect to x and y

df_dx = diff(f, x);

df_dy = diff(f, y);

% Solve the system of equations df_dx = 0 and df_dy = 0 to find the stationary points

[stationary_points_x, stationary_points_y] = solve(df_dx == 0, df_dy == 0);

% Evaluate the function f(x,y) at the stationary points

stationary_point_values = subs(f, [x y], [stationary_points_x stationary_points_y])

% Display the results

disp("Stationary Points:")

disp([stationary_points_x stationary_points_y])

disp("Function Values at Stationary Points:")

disp(stationary_point_values)

Undefined function 'syms' for input arguments of type 'char'.

Stationary Points:

[ 0, 0]

Function Values at Stationary Points:

[ 5]

Unrecognized function or variable 'Stationary'.

[reman]

Find the stationary points of the function f(x, y) = 8x 2 + 6y 2 −2y 3 + 5 and its function values. with matlab code

[reman]

Find the stationary points of the function f(x, y) = 8x 2 + 6y 2 −2y 3 + 5 and its function values. with matlab code

Answer 1

[Jorge Herrera]

Hello there! I recomend you to use diff and solve functions available in Matlab.

To diff function: http://www.mathworks.com/help/matlab/ref/diff.html to solve function: http://www.mathworks.com/help/symbolic/solve.html

Check the examples to get more info about it, I suppose that you know the calculus theory, then solve the problem should be more less easy. If you have problems I'll help you.

Answer 2

[reman]

Find the stationary points of the function f(x, y) = 8x 2 + 6y 2 −2y 3 + 5 and its function values. with matlab code