the graphs of y=x^2(x+1) and y= 1/x(x0) intersect at one point x=r. use Newton's method to estimate the value of r to four decimal places.

Question

the graphs of y=x^2(x+1) and y= 1/x(x>0) intersect at one point x=r. use Newton's method to estimate the value of r to four decimal places.

anonymous · Answer

They intersect in two points, see http://www.wolframalpha.com/input/?i=plot+%28x%5E2+%28x+%2B+1%29+%2C+1%2Fx%29 Which one do you want

anonymous · Answer

To check your answer, visit http://www.wolframalpha.com/input/?i=nsolve+x%5E2+%28x+%2B+1%29+%3D1%2Fx+

anonymous · Answer

Newton's Method for
$$
f(x)=x^2 (x+1)-\frac{1}{x}\
x_0=.7\
x_1= x_0- \frac{f(x_0)}{f'(x_0)}= 0.821277\
x_2= x_1- \frac{f(x_1)}{f'(x_1)}= 0.819174\
x_3= x_3- \frac{f(x_3)}{f'(x_3)}= 0.819173\
$$

anonymous · Answer

If you start from -.7, you obtain the negative root. The sequence of approximate roots is
{-0.7, -1.44643, -1.38359, -1.38029, -1.38028, -1.38028}