Let f be a differentiable function, defined for all real numbers x, with the following properties
(i) f '(x) = ax^2 + bx
(ii) f '(1) = 6 and f "(1) = 18
(iii) int(f(x),x,1,2) = 18
Find f(x). Show your work.
I finally found the lyrics sheet I was looking for in my desk, so my students have had the dubious honor of singing this song in class! Since I mentioned it on the ListServ, I have been asked several times for the words, but I haven't had a chance to share them until now. What follows are the long, sought-after lyrics: