By graphical method show that (x-1)^2 - ln(x)=0 has a unique root in (1,2). (x=1

Question

By graphical method show that (x-1)^2 - ln(x)=0 has a unique root in (1,2).

(x=1 is also a root)

b) Which point 1 or 2 should you start from to make sure the convergence in Newton method?

c) Matlab: Check if Matlab has a function to find roots. If so find the roots of the function above.

Comment:

I need help with the Matlab part

Thank you

Explanation / Answer

x = 0.05; x_old = 100; x_true = 0.0623776; iter = 0; while abs(x_old-x) > 10^-3 && x ~= 0 x_old = x; x = x - (x^3 - 0.165*x^2 + 3.993*10^-4)/(3*x^2 - 0.33*x); iter = iter + 1; fprintf('Iteration %d: x=%.20f, err=%.20f ', iter, x, x_true-x); pause; end

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