(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use Newton's method to find the coordinates of the inflection point of the curve y = e^cosx, 0 <= x <= pi, correct to six decimal places.

2. Relevant equations

None.

3. The attempt at a solution

I calculated y'' (as f(x) in newton formula) and y''' (as f'(x) in newton formula), as they wanted to find the coordinates of the inflection point (when y'' = 0).

y' = -e^(cosx) * sinx

y'' = e^(cosx) * ( sinx^(2) - cosx )

y''' = e^(cosx) * sinx( cosx^2 + 3cosx )

I then subbed in y'' and y''' into the newton equation and this is where I am having trouble, since when ever I try to use an initial approximation e.g. x1 = 0 or x1 = pi, f'(x1) = 0 which is undefined (from x1 = x2 + f(x1) / f'(x1)

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# Newton's method

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