How to find the maximum value of a function?

The function is:

f=sin(x)+sin(x*2)

and I want to find the scalar maximum and this is my code as of now.

f = sin(x)+sin(x*2);
f2 = diff(f,x)==0;
x = solve(f2,x);
X = max(x);

However this code gives:

acos(- 33^(1/2)/8 - 1/8)

and I want a numerical value because I need to use the scalar maximum for other calculations. If I procede with this code then "acos(- 33^(1/2)/8 - 1/8)" shows in every following calculation. Please let me know how to convert this or use a different code, thanks.

Answer 1

[Walter Roberson]

You are chasing the wrong problem.

x = solve(f2,x);

Those are not solutions to when the function f becomes 0: those are the solutions to when the derivative becomes 0. They are the locations of the inflection points, but they are not the values of the functions. You should be using

syms x
f = sin(x)+sin(x*2);
f2 = diff(f,x)==0;
extreme_points = solve(f2,x);
extreme_values = subs(f, x, extreme_points);
[maxX, maxidx] = max(extreme_values);

best_location = extreme_points(maxidx);
best_value = simplify(maxX, 'steps', 50);

best_value =
((3*2^(1/2) + 66^(1/2))*(33^(1/2) + 15)^(1/2))/32

Chances are that you should not be working with numeric values, as the numeric values are only approximations. You might choose to display a numeric value to make it easier for the user to make sense of the result, but you should compute based upon the full result.

To convert to a numeric approximation, double(best_value)

[Josh Belandres]

Thank you so much for your response

[Kareem Dawood]

Thank you for this contribution man!

Answer 2

[KurtanWagner]

Can you graph this as well?

[KurtanWagner]

I got this max value, but I would like to see just how big my variable is

[Walter Roberson]

syms x
f = sin(x)+sin(x*2);
f2 = diff(f,x)==0;
extreme_points = solve(f2,x);
extreme_values = subs(f, x, extreme_points);
[maxX, maxidx] = max(extreme_values);

best_location = extreme_points(maxidx);
best_value = simplify(maxX, 'steps', 50);

fplot(f, [-10 5])
hold on
plot(double(best_location), double(best_value), 'r*');
hold off

.. it is periodic. With a little change to the code you can show that it repeats every 2*pi

Answer 3

[MANSUR]

syms x
f = sin(x)+sin(x*2);
f2 = diff(f,x)=0;

Incorrect use of '=' operator. Assign a value to a variable using '=' and compare values for equality using '=='.

extreme_points = solve(f2,x);
extreme_values = subs(f, x, extreme_points);
[maxX, maxidx] = max(extreme_values);

best_location = extreme_points(maxidx);
best_value = simplify(maxX, 'steps', 50);

fplot(f, [-10 5])
hold on
plot(double(best_location), double(best_value), 'r*');
hold off

[Walter Roberson]

syms x
f = sin(x)+sin(x*2);
f2 = diff(f,x)==0;
extreme_points = solve(f2,x);
extreme_values = subs(f, x, extreme_points);
[maxX, maxidx] = max(extreme_values);

best_location = extreme_points(maxidx);
best_value = simplify(maxX, 'steps', 50);

fplot(f, [-10 5])
hold on
plot(double(best_location), double(best_value), 'r*');
hold off