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Find two points with opposite x-values?

  1. Nov 20, 2011 #1
    1. The problem statement, all variables and given/known data

    Two points on the curve y = x^3 / (1 + x^4) have opposite x-values, x and -x. Find the points making the slope of the line joining them greatest.

    2. Relevant equations

    Not certain which equations I'd need here, because I don't know how to begin solving this...

    3. The attempt at a solution

    I got nothin'. :( I'm really puzzled by this one and don't even know how to start to solve it.

    I thought of taking the derivative and finding the critical points (maxima/minima), then seeing if they had opposite x-values, but that certainly wouldn't work, it doesn't even make sense.

    Do I need to graph the function and figure it out from that? Somehow I get the feeling that I can solve this without graphing it, though.

    I'm definitely not asking for a solution because I want to understand this problem... just point me in the right direction to get started? I'd appreciate it very much! Thank you!
     
  2. jcsd
  3. Nov 20, 2011 #2

    CompuChip

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    You are asked about the line joining the points at (x, f(x)) and (-x, f(-x)) on the graph of the function [itex]f(x) = x^3 / (1 + x^4)[/itex].
    So how about you try to write down the equation of that line?
    In fact, let's start by finding the slope.
     
  4. Nov 20, 2011 #3
    Thanks CompuChip! I did what you suggested and ended up getting x^2 / (1 + x^4) as the slope of the line, and y = (x^2 / (1 + x^4))x + b as the equation of the line.

    Still not seeing what I need to do next, though. :( I'm not understanding how to find b, or how I get x and -x out of this...
     
  5. Nov 20, 2011 #4

    Ray Vickson

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    The question asked you to find the maximum slope.

    RGV
     
  6. Nov 20, 2011 #5
    Do I need to start by taking the derivative? I found the slope of the line joining x and -x, and now I'm not sure what to do with it.
     
  7. Nov 20, 2011 #6
    You know a function for the slope. Maybe you know a way to find the maxima of a function?
     
  8. Nov 27, 2011 #7
    Sorry for replying so late to you all - I ignored my homework over Thanksgiving break, lol - but just wanted to say that I finally figured out how to solve this problem. YAY. Thank you so much to everyone who nudged me in the right direction. :D
     
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