(a) Explanation Given Information: The provided function is E ( t ) = 0.000772 t 3 − 0.0760 t 2 + 1.83 t + 87.3 . Formula used: Set the first derivative of the function to zero, f ' ( x ) = 0 , to find the critical values of the function. Calculation: Consider the function E ( t ) = 0.000772 t 3 − 0.0760 t 2 + 1.83 t + 87.3 . Calculate the first derivative of the function E ( t ) = 0.000772 t 3 − 0.0760 t 2 + 1.83 t + 87.3 . E ′ ( t ) = 0.002316 t 2 − 0.152 t + 1.83 Set the first derivative equal to 0. 0.002316 t 2 − 0.152 t + 1.83 = 0 Use discriminant method x = − b ± b 2 − 4 a c 2 a to solve 0 (b) To determine The classification and interpretation of the critical points of the function E ( t ) = 0.000772 t 3 − 0.0760 t 2 + 1.83 t + 87.3 .

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 10.2, Problem 41E

(a)

To determine

To calculate: The critical points of the function E(t)=0.000772t3−0.0760t2+1.83t+87.3. This model represents energy used from 1985 to 2035 by U.S. Department of energy where t is in years.

(b)

To determine

The classification and interpretation of the critical points of the function E(t)=0.000772t3−0.0760t2+1.83t+87.3.

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Chapter 10.2, Problem 40E

Chapter 10.3, Problem 1CP

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Chapter 10 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 10.1 - 1. The x- values of critical points are found...Ch. 10.1 - Prob. 2CP Ch. 10.1 - Prob. 3CP Ch. 10.1 - Prob. 4CP Ch. 10.1 - In Problems 1 and 2, use the indicated points on...Ch. 10.1 - In Problems 1 and 2, use the indicated points on...Ch. 10.1 - 3. Use the graph of in Problem 1 to identify at...Ch. 10.1 - 4. Use the graph of in Problem 2 to identify at...Ch. 10.1 - In Problems 5 and 6, use the sign diagram for to...Ch. 10.1 - In Problems 5 and 6, use the sign diagram for to...

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The critical points of the function E ( t ) = 0.000772 t 3 − 0.0760 t 2 + 1.83 t + 87.3 . This model represents energy used from 1985 to 2035 by U.S. Department of energy where t is in years.

Solution Summary: The author explains how to calculate the critical values of the function E(t). The model represents energy used from 1985 to 2035 by U.S. Department of Energy.