Profit Function for Producing Thermometers 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. (Enter your answer using interval notation.) P(x) = −0.004x2 + 6x − 5,000 Increasing: Decreasing:

Increasing:

Decreasing:

Step-by-step explanation:

Critical points:

The critical points of a function f(x) are the values of x for which:

For any value of x, if f'(x) > 0, the function is increasing. Otherwise, if f'(x) < 0, the function is decreasing.

The critical points help us find these intervals.

In this question:

So

Critical point:

We have two intervals:

(0, 750) and

(0, 750)

Will find P'(x) when x = 1

Positive, so increasing.

Interval

Will find P'(x) when x = 800

Negative, then decreasing.

Increasing:

Decreasing:

4

step-by-step explanation: