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Maximum Value of a Function and Decreasing Function

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In recession, congress decided to stimulate the economy by providing funds to hire unemployed workers for gov. projects. Suppose the t months after the stimulus programs have begun, there are N(t) thousand people unemployed, where:

N(t)= -t^3 + 45t^2+408t + 3078

a). What is the max # of unemployed workers?
When does the minimum level of unemployment happen?

b)In order to avoid over-stimulating the economy, a decision was made to terminate the program as soon as the rate of unemployment begins to decline. When does this occur?
At this time, how many people are unemployed?

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Solution Summary

Maximum value of a function and a decreasing function are investigated.

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N(t)= -t^3 + 45t^2+408t + 3078

a) What is the max # of unemployed workers?
N'(t) = 0
Or -3t2 + 90t + 408 = 0
Or t2 - 30t - 136 = 0
Or t2 - ...

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