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