# Thread: Intercepts of two graphs

1. ## Intercepts of two graphs

y= arctan x
y= πx^4

Can anyone show me how to find the 2 points that it intersects by hand (calculations)? I tried it by doing arctan x = πx^4 but got confused.

2. Originally Posted by Rui
y= arctan x
y= πx^4

Can anyone show me how to find the 2 points that it intersects by hand (calculations)? I tried it by doing arctan x = πx^4 but got confused.
You aren't getting confused, you are faced with an impossible situation. You can't solve that equation in general. We can, however, pick out x = 0 as a solution fairly easily. There may well be a clever way to ferret out the other solution, but I doubt it.

-Dan

3. Originally Posted by Rui
y= arctan x
y= πx^4

Can anyone show me how to find the 2 points that it intersects by hand (calculations)? I tried it by doing arctan x = πx^4 but got confused.
Though you can't find this point exactly, you can at least put some bounds on it, if you want to play around with it.

$arctan(1) = \frac{\pi}{4} < \pi 1^4$

$arctan(\frac{1}{\sqrt{3}}) = \frac{\pi}{6} > \pi (\frac{1}{\sqrt{3}})^4 = \frac{\pi}{9}$