# Derivatives for functions

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The percent of mothers who work outside the home and have children younger than age 6 yr is approximated by the following function where t is measured in years, with t = 0 corresponding to the beginning of 1980.

P(t) = 34.57(t + 3)0.205 (0 t 21)

Compute the following value. Round your answer to 4 decimal places.

P''(18) =

During testing of a certain brand of air purifier, the amount of smoke remaining (as a percent of the original amount) t min after the start of the test was given by the following function.

A(t) = -0.00006t5 + 0.00468t4 - 0.132t3 + 1.7t2 - 17.63t + 107

Compute the following values.

A'(10) =

A''(10) =

(b) Compute the following values. (Round your answer to four decimal places.)

C '(5000) =

C '(10,000) =

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The solution provides examples on how to perform derivatives for some functions.

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The percent of mothers who work outside the home and have children younger than age 6 yr is approximated by the following function where t is measured in years, with t = 0 corresponding to the beginning of 1980.

P(t) = 34.57(t + 3)0.205 (0 t 21)

Compute the following ...

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