If you were given a function D(x) which estimates the average listenership of a radio station x hours after programming begins each day. If you were given a function D(x) which estimates the average listenership of a radio station x hours after programming begins each day. Describe how would you go about determining the time of peak listenership between the programming starts at 6 a.m to 2 p.m
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Given: the function D(x) describes the average listenership and D(x) is dependent on the time of day (x) after programming begins eacy day.
There are two ways to determine the answer:
1. Graph the equation of listenership v. time and determine where the maximum listenership exists along the time axis.
2. Asssuming that D(x) is a continuous function and does not have discontinuities throughout the day, then another way to determine peak listenership is to take the derivative of D(x), and then set the derivative equal to zero, and solve for x.
D'(x) = 0
Solving the derivative for x leads to a local maximum or minimum value. Determining whether the x value is a maximum or minimum can be determined by taking the second derivative, D''(x), and checking the sign of the second derivative.
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