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 . Find the intervals where the profit function P is increasing and the intervals where P is decreasing.
A)increasing on , decreasing on
B)increasing on , decreasing on
C)increasing on , decreasing on
D)increasing on , decreasing on
E)increasing on , decreasing on

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  . Find the intervals where the profit function P is increasing and the intervals where P is decreasing.
A)increasing on , decreasing on 
B)increasing on , decreasing on 
C)increasing on , decreasing on 
D)increasing on , decreasing on 
E)increasing on , decreasing on

Quizplus · Accepted Answer

The profit function is not given, so we cannot find its derivative directly. However, we can use the fact that the statement "the profit function is increasing" means that the derivative of the profit function is positive, and the statement "the profit function is decreasing" means that the derivative of the profit function is negative. Let P(x) be the profit function for x units of thermometers. Then, we know that P'(x) > 0 for 0 < x < 700 (since the profit function is increasing on this interval). Similarly, P'(x) < 0 for x > 700 (since the profit function is decreasing on this interval). Therefore, the intervals where the profit function P is increasing and the intervals where P is decreasing are: Increasing: 0 < x < 700 Decreasing: x > 700 The only answer choice that matches these intervals is C: increasing on 11eb12b0_a9f9_17a2_b394_15d02a435562_TB7866_11, decreasing on 11eb12b0_a9f9_17a3_b394_ddb241a2f73b_TB7866_11.

The Mexican Subsidiary of ThermoMaster Manufactures an Indoor-Outdoor Thermometer