help me with optimization for calculus

Question

anonymous · Answer

a computer company determines its profit equation in millions of dollars given by p=x^3-48x^2+720x-1000 where x is  the number of thousands of units of software sold

anonymous · Answer

and 0<x<40 optimize the manufactures profit

goten77 · Answer

im thinking this is really ez.... but maybe im wrong.... since from 0-40 it looks like a line almost.... wouldnt (40,y) b the maximum?

goten77 · Answer

or maybe im wrong

zepdrix · Answer

|dw:1355889094401:dw|It's a cubic function, so it's going to have this shape. As I've illustrated in the picture, it is possible that 40 might not be the maximum profit value. So we'll have to do some work to find out where that point is.