A manufacturer sells telephones with cost function C(x) = 7.4x - .0002x2 , 0≤x≤ 600 and revenue function R(x) = 9.2x - .002x2 , 0≤x≤ 600. Determine the interval(s) on which the profit function is increasing?

If the profit function p(x) can be given by
  p(x) = r(x) - c(x)
  = (9.2x - 0.002x^2) - (7.4x - 0.0002x^2)
  = 1.8x - 0.0018x^2
It will be increasing when its derivative is more than zero
  dp/dx > 0
  1.8 - 0.0036x > 0
  1.8 > 0.0036x
  1.8/0.0036 > x
  x < 500

The profit function will be increasing on the interval [0, 500), that is 0 ≤ x < 500.