math
posted by jordan on .
the profits of Mr/ Lucky's company can be represented by the equation y=3x^2+18x4, where y is the amount of profit in hundreds of thousands of dollars and x is the number of years of operation. He realizes his company is on the downturn and wishes to sell it before he ends up in debt.
a) when will Unlicky's buisness show the maximum of profit?
b)what is the maximum profit?
c)at what time will it be too late to sell his business?(when will he start losing money?)

Given:
f(x)=3x^2+18x4
a)
Find f'(x) and equate to zero.
solve for x=xm.
Since the leading coefficient is 3, the extremum is a maximum.
b) maximum profit=f(xm)
c) He starts losing money when f(x)=0, AND f'(x)<0. There are two roots to f(x)=0, make sure the correct one is chosen.