Apply the Newton-Raphson's method xn+1 = xn – f '(xn) / f ''(xn) to develop a function double findMinMax(…) that returns a solution that is either a minimum value or a maximum value for z. The program finds a local minimum or a local maximum when the difference between the new solution and the previous one is smaller than 0.00001 within 10000 iterations. Otherwise, it shows Infinity as output. Let function z = x4+2y6 – xy – x + 2. Show the post-conditions for z. The preconditions for x and y are shown as below. Feel free to choose an arbitrary initial guess values x0 and y0 that meet the following precondition. |x| ≤ 6 and |y| ≤ 5
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Apply the Newton-Raphson's method xn+1 = xn – f '(xn) / f ''(xn) to develop a function double findMinMax(…) that returns a solution that is either a minimum value or a maximum value for z. The program finds a local minimum or a local maximum when the difference between the new solution and the previous one is smaller than 0.00001 within 10000 iterations. Otherwise, it shows Infinity as output.
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- Let function z = x4+2y6 – xy – x + 2. Show the post-conditions for z.
The preconditions for x and y are shown as below. Feel free to choose an arbitrary initial guess values x0 and y0 that meet the following precondition.
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- |x| ≤ 6 and |y| ≤ 5
Given
The answer is given below.
As per the question,we have to construct a function findMinMax(...) which will return the maximum /minimum value of the given 2d function
Then we have to test this function using the given example:
z=x^4+2y^6-xy-x+2
with initial values of X,Y such that:|x|<=6 & |y|<=5
Here we will take:x0=y0=1
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