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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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.

\[
f'(-9) = \boxed{\phantom{0}}
\]

\[
f'(1) = \boxed{\phantom{0}}
\]
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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