Hello everyone, I hope you can help me out. I'm typing this in a rush so please forgive me for not using LaTeX. Here is the problem:
Given the function f(x)=-0.00128x^3+0.144x^2-4.4x+60, find the point on f(x) whose coordinates have the greatest possible product.
If it's gonna be any help, here are the coefficients in fraction form (in the same order): -4/3125, 18/125, -22/5, and 60.
The graph does not pass through QIV, so I'm assuming the required point is in QI because points in QII and QIII have coordinates with opposite signs and points on the axes have at least one zero coordinate. That's easy enough, but I'm stumped beyond that point. Help in any form would be greatly appreciated. Thank you very much!
PS This is not a school assignment. I'm working as a math editor for a textbook publishing company. This problem came up, and I have to crack it to make sure that the problem is solvable. Too bad I don't see how it can be done. I really hope you can help me, but more than that, I hope this post doesn't get junked for violating Brilliant guidelines. Thanks again!