using newtons method solve f(x)=x4 -x3+4x2-cos(x) for 5 iterations in matlab

To use Newton's method to solve the equation f(x) = x^4 - x^3 + 4x^2 - cos(x), you can follow these steps in MATLAB:

  1. Define the function f(x) as a MATLAB function:
main.m
function y = f(x)
    y = x^4 - x^3 + 4*x^2 - cos(x);
end
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  1. Define the derivative of f(x) as another MATLAB function:
main.m
function y = df(x)
    y = 4*x^3 - 3*x^2 + 8*x + sin(x);
end
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  1. Choose an initial guess, let's say x0 = 0.

  2. Iterate the following formula for 5 iterations (or any desired number of iterations):

main.m
x = x0;
for i = 1:5
    x = x - f(x) / df(x);
end
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After the 5 iterations, the variable x will contain the approximate solution to the equation f(x) = 0 using Newton's method.

Note that the above code assumes that the Newton's method will converge to a solution. If the function has multiple solutions or the initial guess is not close enough to a solution, the method may not converge or converge to a different solution.

Also, make sure to adjust the number of iterations, initial guess, and any other parameters as needed for your specific problem.

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