Explanation Given: The function is: f ( t ) = 13 t e − t 2 + 3.6 . Formula used: Write the formula for derivative of power rule. If f ( x ) = x n for any number n , then the derivative. f ′ ( x ) = n x n − 1 If f ( x ) = k for any real number k , then the derivative is defined by the formula. f ′ ( x ) = 0 Write the formula for derivative of exponents. f ( x ) = e n x for any number n , then the derivative. f ′ ( x ) = n e n x If the function is given as f ( x ) = u ( x ) . v ( x ) , then the derivative of the function f ( x ) by product rule is, f ′ ( x ) = u ( x ) . v ′ ( x ) + v ( x ) . u ′ ( x ) Here, v ( x ) is the function of x and v ′ ( x ) is the derivative of the function v ( x ) . To find local maximum and minimum calculate the values of x from the equation, f ′ ( x ) = 0 . Then find f ″ ( x ) and substitute the values of x . If f ″ ( x ) equals some positive quantity then the local minimum is located at that point x and if f ″ ( x ) equals some negative quantity then the local maximum is located at that point. Calculation: Consider the given function: f ( t ) = 13 t e − t 2 + 3.6 …… (1) Differentiate f ( t ) with respect to t . d d t ( f ( t ) ) = d d t ( 13 t e − t 2 + 3.6 ) f ′ ( t ) = 13 ( d d t ( t e − t 2 ) ) + d d t ( 3.6 ) f ′ ( t ) = 13 ( t d d t ( e − t 2 ) + e − t 2 d d t ( t ) ) + 0 f ′ ( t ) = 13 ( t ( e − t 2 ( − 1 2 ) ) + e − t 2 ( 1 ) ) Solve further as, f ′ ( t ) = 13 ( − t e − t 2 2 + e − t 2 )

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ISBN: 9780135240687

Author: Lial

Publisher: PEARSON

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Chapter 12.3, Problem 38E

To determine

To calculate: The following if the unemployment rates for individuals age 20 to 24 years from the year 2008 to 2016 are given by the function f(t)=13te−t2+3.6; 0≤t≤8, where t=0 stands for the year 2008,

a. How many years after 2008 was the unemployment rate for people aged 20 to 24 years maximum?

b. What was the maximum unemployment rate for this group?

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Chapter 12.3, Problem 37E

Chapter 12.3, Problem 39E

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Solution Summary: The author explains how to calculate the maximum unemployment rate for 20 to 24 year olds, based on the function f(t)=13t

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