Explanation Proof: The percentage of the U.S. population that is obese is approximated by the function, P ( t ) = 0.0004 t 3 + 0.0036 t 2 + 0.8 t + 12 Here, 0 ≤ t ≤ 13 , t is measured in years, and t = 0 corresponds to the beginning of 1991. The rate of change of percentage of U.S. population that is obese is the derivative of the function P ( t ) = 0.0004 t 3 + 0.0036 t 2 + 0.8 t + 12 . The derivative of the function P ( t ) is, P ′ ( t ) = d d t ( 0.0004 t 3 + 0.0036 t 2 + 0.8 t + 12 ) = d d t 0.0004 t 3 + d d t 0.0036 t 2 + d d t 0.8 t + d d t 12 ( d d x [ f ( x ) ± g ( x ) ] = d d x [ f ( x ) ] ± d d x [ g ( x ) ] ) = 0.0004 d d t t 3 + 0.0036 d d t t 2 + 0.8 d d t t + 0 ( d d x [ c f ( x ) ] = c d d x [ f ( x ) ] ) = 0.0004 ( 3 t 3 − 1 ) + 0.0036 ( 2 t 2 − 1 ) + 0.8 ( 1 t 1 − 1 ) ( d d x ( x ) n = n x n − 1 ) Simplify it further. P ′ ( t ) = 0.0004 ( 3 t 2 ) + 0.0036 ( 2 t ) + 0.8 ( t 0 ) = 0.0012 t 2 + 0.0072 t + 0.8 The rate of the rate of change of the percent of the U.S population that is deemed obese is the second derivative of the function P ( t ) . The second derivative of the function is, P ″ ( t ) = d d t P ′ ( t ) = d d t ( 0.0012 t 2 + 0.0072 t + 0.8 ) = d d t 0

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Author: Tan

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Chapter 3.5, Problem 37E

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To show: The rate of rate of change of the percent of the U.S population that is deemed obese was positive from 1991 to 2004, and its interpretation.

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Chapter 3.5, Problem 36E

Chapter 3.5, Problem 38E

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The rate of rate of change of the percent of the U.S population that is deemed obese was positive from 1991 to 2004, and its interpretation.

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