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Math Help - Intercepts of two graphs

  1. #1
    Rui
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    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.


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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Rui View Post
    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
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  3. #3
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    Quote Originally Posted by Rui View Post
    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}
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