Consider the following function. \( f(x) = -x^2 - 18x - 1 \) Find its average rate of change over the interval \([-9, 1]\). \[ \frac{\Delta y}{\Delta x} = \boxed{\phantom{0}} \] Compare this rate with the instantaneous rates of change at the endpoints of the interval. \[ f'(-9) = \boxed{\phantom{0}} \] \[ f'(1) = \boxed{\phantom{0}} \]
Consider the following function. \( f(x) = -x^2 - 18x - 1 \) Find its average rate of change over the interval \([-9, 1]\). \[ \frac{\Delta y}{\Delta x} = \boxed{\phantom{0}} \] Compare this rate with the instantaneous rates of change at the endpoints of the interval. \[ f'(-9) = \boxed{\phantom{0}} \] \[ f'(1) = \boxed{\phantom{0}} \]
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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Question
![Consider the following function.
\( f(x) = -x^2 - 18x - 1 \)
Find its average rate of change over the interval \([-9, 1]\).
\[
\frac{\Delta y}{\Delta x} = \boxed{\phantom{0}}
\]
Compare this rate with the instantaneous rates of change at the endpoints of the interval.
\[
f'(-9) = \boxed{\phantom{0}}
\]
\[
f'(1) = \boxed{\phantom{0}}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03b8de10-db72-4871-992f-83fe241163fb%2Fdf810b27-8095-4ae6-9651-bc02d7f105dd%2Fuj49af_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following function.
\( f(x) = -x^2 - 18x - 1 \)
Find its average rate of change over the interval \([-9, 1]\).
\[
\frac{\Delta y}{\Delta x} = \boxed{\phantom{0}}
\]
Compare this rate with the instantaneous rates of change at the endpoints of the interval.
\[
f'(-9) = \boxed{\phantom{0}}
\]
\[
f'(1) = \boxed{\phantom{0}}
\]
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