Find the average value of the function f(x) = over the interval [0, 6] and find c such that f (c) equals the average value of the function over [0, 6].
Find the average value of the function f(x) = over the interval [0, 6] and find c such that f (c) equals the average value of the function over [0, 6].
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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![### Checkpoint 1.14
Find the average value of the function \( f(x) = \frac{x}{2} \) over the interval \([0, 6]\) and find \( c \) such that \( f(c) \) equals the average value of the function over \([0, 6]\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11c3e735-47a2-4be2-bcf0-76944b0744ea%2Fa9dc144f-4747-408b-abfb-f2656fdaa402%2Fuklihs_processed.png&w=3840&q=75)
Transcribed Image Text:### Checkpoint 1.14
Find the average value of the function \( f(x) = \frac{x}{2} \) over the interval \([0, 6]\) and find \( c \) such that \( f(c) \) equals the average value of the function over \([0, 6]\).
![**Checkpoint 1.15**
Given \[ \int_{0}^{3} (2x^2 - 1) \, dx = 15 \], find \( c \) such that \( f(c) \) equals the average value of \( f(x) = 2x^2 - 1 \) over \([0,3]\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11c3e735-47a2-4be2-bcf0-76944b0744ea%2Fa9dc144f-4747-408b-abfb-f2656fdaa402%2Fauszg3_processed.png&w=3840&q=75)
Transcribed Image Text:**Checkpoint 1.15**
Given \[ \int_{0}^{3} (2x^2 - 1) \, dx = 15 \], find \( c \) such that \( f(c) \) equals the average value of \( f(x) = 2x^2 - 1 \) over \([0,3]\).
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