matlab root finding function

To find the root of a function in MATLAB, you can use the built-in function fzero(). The fzero() function is used to find a root of a given function within a specified interval.

Here is the syntax for using the fzero() function:

x = fzero(fun, x0)

• fun is the function for which you want to find the root.
• x0 is the initial guess for the root.

The fzero() function returns the approximate root of the function fun.

For example, let's say you want to find the root of the function f(x) = x^2 - 4 starting from an initial guess of x0 = 1. You can define the function and use the fzero() function as follows:

fun = @(x) x^2 - 4;
x0 = 1;
x = fzero(fun, x0);

In this case, the value of x will be approximately 2, which is the root of the function f(x) = x^2 - 4.

Note that the fzero() function requires an initial guess that is close to the root in order to converge to the correct solution. If you provide a poor initial guess, the function may fail to find the root or find a different root altogether.

You can also specify additional options and constraints when using the fzero() function, such as the maximum number of iterations or the tolerance for convergence. You can refer to the MATLAB documentation for more details on these options.

I hope this explanation helps you understand how to use the fzero() function in MATLAB for root finding.