Science:Math Exam Resources/Courses/MATH100/December 2010/Question 01 (m)/Solution 1

Let us first compute the derivative

$\displaystyle f'(x)=e^{x}-2x$

and now crank up the algorithm.

${\begin{aligned}x_{2}&=x_{1}-{\frac {f(x_{1})}{f'(x_{1})}}\\&=0-{\frac {1}{1}}=-1\\x_{3}&=x_{2}-{\frac {f(x_{2})}{f'(x_{2})}}\\&=-1-{\frac {e^{-1}-1}{e^{-1}+2}}\\&={\frac {-1-2e^{-1}}{2+e^{-1}}}\end{aligned}}$