Coding must be done in MATLab

3) (13 pts) Newton-Raphson

a(1) Find the derivative of the equation in 1c. I expect an exact, analytical answer to be included cleanly in the PDF report. Learn to use a formula editor, or at least write neatly and scan it.

1c equation: function f=f(x) f= x^10 - 10*x^5 +0.4*x - 0.4

b(3) Write a N-R root solver. Inputs should be an initial guess, function handle, analytical derivative handle, desired approximate relative error threshold, and max number of iterations. Return values should be root location (value of x where f(x)~0) and number of iterations. Feel free to start with a copy of Bisection.m, re-purposed (AND re-documented) for this problem.

c(3) Use the function to find the roots, with initial values chosen as appropriate (and documented in your PDF).

d(3) Pick one root. For that root only, compare the number of iterations to the bisection method I've given you, for the same tolerance. Try to make it a fair comparison (remember one is bracketing and one is open, so perhaps you should start N-R at one of the bracket edges?)

e(3) Use Linspace or something similar to produce a plot of which root is found over the interval [-5,4.5]. Does N-R always find the closest root? Find at least one spot where odd behavior happens, and explain it in words.