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Find the average value of the function y = 35 - 2x on the interval [0, 4]. O 31 10 O 20 O None of the others are correct O 15 O 27 4x0

Find the average value of the function y = 35 - 2x on the interval [0, 4]. O 31 10 O 20 O None of the others are correct O 15 O 27 4x0

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem Statement:** Find the average value of the function \( y = 35 - 2x \) on the interval \([0, 4]\). **Options:** - \( 31 \) - \( 10 \) - \( 20 \) - None of the others are correct - \( 15 \) - \( 27 \) **Explanation:** To find the average value of a continuous function \( f(x) \) on an interval \([a, b]\), use the formula: \[ \text{Average value} = \frac{1}{b-a} \int_{a}^{b} f(x) \, dx \] In this case, let's apply it to find the average value of \( y = 35 - 2x \) from \( x = 0 \) to \( x = 4 \).
Transcribed Image Text:**Problem Statement:** Find the average value of the function \( y = 35 - 2x \) on the interval \([0, 4]\). **Options:** - \( 31 \) - \( 10 \) - \( 20 \) - None of the others are correct - \( 15 \) - \( 27 \) **Explanation:** To find the average value of a continuous function \( f(x) \) on an interval \([a, b]\), use the formula: \[ \text{Average value} = \frac{1}{b-a} \int_{a}^{b} f(x) \, dx \] In this case, let's apply it to find the average value of \( y = 35 - 2x \) from \( x = 0 \) to \( x = 4 \).
**Problem Statement:** Let the function \( r(t) \) represent the rate at which a family's savings is growing. Select the interpretation of the expression \(\int_{2016}^{2021} r(t) \, dt\). **Options:** - O None of the others are correct - O Savings of the family in 2021 - O Change in savings rate between 2016 and 2021 - O Rate of savings in 2021 - O Average rate of change of the savings rate between 2016 and 2021 - O Total increase in savings between 2016 and 2021 **Navigation Buttons:** - Previous - Next
Transcribed Image Text:**Problem Statement:** Let the function \( r(t) \) represent the rate at which a family's savings is growing. Select the interpretation of the expression \(\int_{2016}^{2021} r(t) \, dt\). **Options:** - O None of the others are correct - O Savings of the family in 2021 - O Change in savings rate between 2016 and 2021 - O Rate of savings in 2021 - O Average rate of change of the savings rate between 2016 and 2021 - O Total increase in savings between 2016 and 2021 **Navigation Buttons:** - Previous - Next
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