# Thread: Newton's method to approximate the intersection...

1. ## Newton's method to approximate the intersection...

Find the third approximation of x3 of Newton's method to approximate the intersection of $\displaystyle y=[\sqrt(x)]+1$ and $\displaystyle y=x^2$.

What do I do? Set them equal to each other?

2. Originally Posted by hazecraze
Find the third approximation of x3 of Newton's method to approximate the intersection of $\displaystyle y=[\sqrt(x)]+1$ and $\displaystyle y=x^2$.

What do I do? Set them equal to each other?
Yes, and then get everything on one side of the equation. That will be the $\displaystyle f(x)$ you need to apply Newton's Method.

Can you take it from here?

3. So I did $\displaystyle f(x)=x^2-\sqrt(x)-1$
$\displaystyle f'(x)= 2x-\frac{1}{2\sqrt(x)}$

I used $\displaystyle x1=1$

$\displaystyle x2= 1 + \frac{1-1-1}{2-.5}$

= .333

$\displaystyle x3=.333 + \frac{-1.466}{-.8660}$

=$\displaystyle 2.0227$
Answer is supposed to be: $\displaystyle 1.50143$

4. I tried it again and now I'm getting 7.68, which is even further from the right answer. What am I doing wrong?

5. ## optimization problem

edit

6. Looks like you made a mistake with a sign
$\displaystyle x2= 1 - \frac{1-1-1}{2-.5}$