Question

The Mexican subsidiary of ThermoMaster manufactures an indoor-outdoor thermometer. Management estimates that the profit (in dollars) realizable by the company for the manufacture and sale of x units of thermometers each week is represented by the function below, where x ≥ 0. Find the interval where the profit function P is increasing and the interval where P is decreasing.
P(x) = -0.002x^2 + 5x - 5000

Answer 1

$P(x) =-0.002x^2+5x-5000\\P'(x)=-0.004x+5=0\\-0.004x=-5\\x=1250$

We can deduce that the graph is a negative parabola from -0.002x^2. Therefore, the graph is increasing < 1250 and decreasing > 1250.

P(x) is increasing from $[0,1250)$ and decreasing from $(1250,\infty]$.