Consider Newton's method to find a minimum or maximum value attained by a function over an...

  

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Consider Newton's method to find a minimum or maximum value attained by a function over an interval. Given a function f, we wish to find max f(x) reab Start with an initial guess, ro, then generate a sequence of guesses using the formula where h is some arbitrary small value. where f' and f" are first and second derivatives. We won't be finding derivatives analytically, instead, we will be using numerical approximations (central finite differences), given by R Python Julia Ik+1= Ik - e 202 We will work with the normal pdf, f(a; , o) = /27 ( . Let u m1936 be the mean Calories per Serving from 1936, and let = $1936 be the corresponding standard deviation. We will wish to find the that maximizes R f'(xk) f" (k) max pdf (x; m1936, 1936) Let the initial guess be ro= 180 and let h = 0.1. Calculate 10 successive k, saving each value in a vector. Print the final k. Why does this value maximize the likelihood function? Python f(x+/)-f(x - 1) h f(x+h)-2f(x) + f(x-h) 2 Julia h (x-) Part b. Plot the sequence of a versus iteration number (k) as the independent variable. Add a horizontal line corresponding to m1936 = 268.1. How many iterations are required until |k+1-k| < 10-6? Consider Newton's method to find a minimum or maximum value attained by a function over an interval. Given a function f, we wish to find max f(x) reab Start with an initial guess, ro, then generate a sequence of guesses using the formula where h is some arbitrary small value. where f' and f" are first and second derivatives. We won't be finding derivatives analytically, instead, we will be using numerical approximations (central finite differences), given by R Python Julia Ik+1= Ik - e 202 We will work with the normal pdf, f(a; , o) = /27 ( . Let u m1936 be the mean Calories per Serving from 1936, and let = $1936 be the corresponding standard deviation. We will wish to find the that maximizes R f'(xk) f" (k) max pdf (x; m1936, 1936) Let the initial guess be ro= 180 and let h = 0.1. Calculate 10 successive k, saving each value in a vector. Print the final k. Why does this value maximize the likelihood function? Python f(x+/)-f(x - 1) h f(x+h)-2f(x) + f(x-h) 2 Julia h (x-) Part b. Plot the sequence of a versus iteration number (k) as the independent variable. Add a horizontal line corresponding to m1936 = 268.1. How many iterations are required until |k+1-k| < 10-6?

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Lets break down the problem into two parts Part A and Part B Part A Calculate the sequence of x values using Newtons method and print the final xk Her... View the full answer