find the roots and the minimum of the function f(x) over the range of 0 ≤ 𝑥 ≤ 4. 𝑓(𝑥) = 0.3𝑥 − sin (2𝑥) verify that your answer is the global minimum. in matlab

To find the roots and the minimum of a function in MATLAB, you can use the roots and fminbnd functions.

First, define the function f(x):

main.m
f = @(x) 0.3 * x - sin(2 * x);
31 chars
2 lines

To find the roots of the function, use the roots function with the coefficients [0.3, -sin(2)]:

main.m
roots([0.3, -sin(2)])
22 chars
2 lines

To find the minimum of the function over the range 0 ≤ x ≤ 4, you can use the fminbnd function:

main.m
minimum = fminbnd(f, 0, 4);
28 chars
2 lines

The fminbnd function returns the value of x at which the function is minimized.

To verify if this is the global minimum, you can plot the function using the ezplot function and visually inspect the graph:

main.m
ezplot(f, [0, 4]);
hold on;
plot(minimum, f(minimum), 'ro');
hold off;
71 chars
5 lines

If the red dot indicates the lowest point on the graph, then the minimum value found is the global minimum.

Please note that ezplot function is deprecated in MATLAB. You can use fplot instead.

main.m
fplot(f, [0, 4]);
hold on;
plot(minimum, f(minimum), 'ro');
hold off;
70 chars
5 lines

Remember to run these commands in MATLAB to obtain the roots and minimum of the function f(x).

Hope that helps!