Consider the function f(x) = (x − 2)^4 + (x − 2)^5. Minimize the function using the iterative method x(k+1) = x(k) − 4f(x(k))/f'(x(k)), with initial guess x(0) = 3. Prove that the method converges quadratically, and determine the rate constant.

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Consider the function f(x) = (x − 2)^4 + (x − 2)^5. Minimize the function using the iterative method x(k+1) = x(k) − 4f(x(k))/f'(x(k)), with initial guess x(0) = 3. Prove that the method converges quadratically, and determine the rate constant.

 
 
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