Question

An entrepreneur estimates that the total profit (profit = total revenue minus total cost) from his proposed company will be given by the function P(x) = x^3 – 4x^2 + 3x – 12, where P is in hundreds of dollars and x is the number of years elapsed after the company starts operations. In how many years (x) will the company reach break-even point (no profit, no loss)?

Answer 1

I found the same problem but with given choices:
A.1 year 
B.2 years 
C.3 years 
D.4 years 
E.6 years

profit = total revenue - total cost
p(x) = x³ - 4x² + 3x - 12

simply plug each choices to solve. answer must be 0.

A) p(1) = 1³ - 4(1²) + 3(1) - 12 = 1 - 4 + 3 - 12 = -12
B) p(2) = 2³ - 4(2²) + 3(2) - 12 = 8 - 16 + 3 - 12 = -17
C) p(3) = 3³ - 4(3²) + 3(3) - 12 = 27 - 36 + 9 - 12 = -12
D) p(4) = 4³ - 4(4²) + 3(4) - 12 = 64 - 64 + 12 - 12 = 0
E) p(6) = 6³ - 4(6²) + 3(6) - 12 = 216 - 144 + 18 - 12 = 78

It would take 4 years for the company to reach break-even point.