Explanation Definition used: First derivative test: Suppose c to be a critical number for a function f . Assume that f is continuous on ( a , b ) and differentiable on ( a , b ) except at c , and c is the only critical number of f in ( a , b ) . f ( c ) is a relative maximum of f at c if f ′ ( x ) > 0 in the interval ( a , c ) and f ′ ( x ) < 0 in the interval ( c , b ) . f ( c ) is a relative minimum f at c if f ′ ( x ) < 0 in the interval ( a , c ) and f ′ ( x ) > 0 in the interval ( c , b ) . Relative maximum: A function is said to have a relative maximum f ( c ) at c if f ′ ( x ) > 0 in the interval ( a , c ) and f ′ ( x ) < 0 in the interval ( c , b ) . Relative minimum: A function is said to have a relative maximum f ( c ) at c if f ′ ( x ) < 0 in the interval ( a , c ) and f ′ ( x ) > 0 in the interval ( c , b ) . Calculation: The Thermic effect of food is given by the function F ( t ) = − 10.28 + 175.9 t e − t 1.3 . Obtain the derivative of the function as follows. F ′ ( t ) = ( − 10.28 + 175.9 t e − t 1.3 ) ′ = 0 + 175.9 ( t e − t 1.3 ( − 1 1.3 ) + e − t 1.3 ) = 175.9 e − t 1.3 ( − t 1.3 + 1 ) Set F ′ ( c ) = 0 and find the value of c . 175.9 e − c 1.3 ( − c 1.3 + 1 ) = 0 175.9 e − c 1

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 13.2, Problem 56E

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To find: The time at which the maximum thermic effect of food is achieved where the thermic effect of food is given by the function F(t)=−10.28+175.9te−t1.3 .

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Chapter 13.2, Problem 55E

Chapter 13.2, Problem 57E

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The time at which the maximum thermic effect of food is achieved where the thermic effect of food is given by the function F ( t ) = − 10.28 + 175.9 t e − t 1.3 .

Solution Summary: The author explains that the age at which the maximum thermic effect of food is attained is 1.3 hours.

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To find: The time at which the maximum thermic effect of food is achieved where the thermic effect of food is given by the function F(t)=−10.28+175.9te−t1.3 .

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