Designing a calculus riddle/scavenger hunt

[blujay]

Hi. I apologize if this is an unwelcome intrusion, but I need help from folks such as yourselves. I know nothing about calculus, but a friend of mine does. I would like to design a kind of riddle or scavenger hunt in the form of a calculus problem which, when solved, would result in a specific number. I'd like it to have a few variables whose values would also be specific, and could be discovered outside of the problem. Specifically, I'd like the final answer to be 11644, one variable to be 1924, another variable to be 1934, and a third to be 1978.

Since I know nothing about calculus, I don't know for certain how skilled my friend is, but being an undergrad math major, I'd expect at least an intermediate level.

The end result of solving this problem will be my friend receiving a gift, so I ask not so much for myself as for my friend. :) Thank you for your consideration.

 

[LCKurtz]

Here's one you might consider:

1. Find the largest prime factor of 9699690 and multiply it by 100
2. Add that to each of the three roots of x³-136x²+5340x-63648.
3. Calculate twice the sum of these three numbers
4. Subtract 28.

If your victim can't complete step 2 give him/her the hint that one root is 24.

 

[blujay]

LCKurtz, thank you kindly for your help. In case you're curious, this is the gift:

http://shirt.woot.com/friends.aspx?k=15303