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A series of free Calculus Videos and solutions. How to solve Concavity Practice Problems?

Concavity Practice Problem 5

Problem: An all news radio station has made a survey of listening habits of local residents between the hours of 5pm and midnight. The survey indicates that the percentage of the local adult population that is tuned in to the station x hours after 5pm is: f(x)=1/8(-2x^3+27x^2-108x+240) a)At what time between 5pm and midnight are the most people listening to the station? What percentage of the population is listening at this time? b) At what time between 5pm and midnight are the fewest people listening? What percentage of the population is listening at this time?

This lecture practices how to analyze function f(x)=x^3-3x^2+3x+1 through increasing, decreasing, concavity, inflection points, critical points, and extremum.

This lecture practices how to analyze function f(x)=x^3(x^2+2x-3) through increasing, decreasing, concavity, inflection points, critical points, and extremum.

This lecture practices how to analyze an epidemic through the increasing, decreasing, concavity, inflection points, critical points, and extremum of the function that models it.

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