11. Find the instantaneous rate of change (derivative) at t = 8. Use the charts below to find the AROC for each interval as part of the process of finding the derivative value. T(t)= = -(t-10)²+105 Interval Average ROC from the left Interval Average ROC from the right [7,8] [8,9] [7.5.8] [8,8.5] [7.9.8] 05 [8.8.1] 25 [7.99, 8] [8.8.01] Write out the derivative at t = 8 and write a sentence describing what this value is in the context of the temperature function.
11. Find the instantaneous rate of change (derivative) at t = 8. Use the charts below to find the AROC for each interval as part of the process of finding the derivative value. T(t)= = -(t-10)²+105 Interval Average ROC from the left Interval Average ROC from the right [7,8] [8,9] [7.5.8] [8,8.5] [7.9.8] 05 [8.8.1] 25 [7.99, 8] [8.8.01] Write out the derivative at t = 8 and write a sentence describing what this value is in the context of the temperature function.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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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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Help!!
![option
H
command
Math 160
Instantaneous rate of change (ROC)
Interval
0161
where lim is the limit symbol and the interval (int) to the left and right of the value
becomes arbitrarily small.
Average ROC
from the left
The Derivative
The derivative at a point is the instantaneous rate of change at a point. Another
way of stating this is:
f'(a) = lim
x→a
where h is the width of the interval.
Interval
Average ROC
from the right
lim AROC = ROC
int-0
f (x) - f(a)
x-a
command
[7,8]
[8,9]
11. Find the instantaneous rate of change (derivative) at t = 8. Use the charts below to
find the AROC for each interval as part of the process of finding the derivative value.
T(t) = -(t-10)² +105
or f'(x) =
option
[7.5,8]
ET
[8,8.5]
Worksheet.
f(x+h)-f(x)mont
h
[7.9,8]
[7.99, 8]
[8.8.1] 19 [8.8.01]
Write out the derivative at t = 8 and write a sentence describing what this value is in
the context of the temperature function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffaa3be14-7f82-4920-95bd-32284dc4e75b%2F14a7f837-2450-4820-81f9-b91f1be54576%2Flr2wmor_processed.jpeg&w=3840&q=75)
Transcribed Image Text:option
H
command
Math 160
Instantaneous rate of change (ROC)
Interval
0161
where lim is the limit symbol and the interval (int) to the left and right of the value
becomes arbitrarily small.
Average ROC
from the left
The Derivative
The derivative at a point is the instantaneous rate of change at a point. Another
way of stating this is:
f'(a) = lim
x→a
where h is the width of the interval.
Interval
Average ROC
from the right
lim AROC = ROC
int-0
f (x) - f(a)
x-a
command
[7,8]
[8,9]
11. Find the instantaneous rate of change (derivative) at t = 8. Use the charts below to
find the AROC for each interval as part of the process of finding the derivative value.
T(t) = -(t-10)² +105
or f'(x) =
option
[7.5,8]
ET
[8,8.5]
Worksheet.
f(x+h)-f(x)mont
h
[7.9,8]
[7.99, 8]
[8.8.1] 19 [8.8.01]
Write out the derivative at t = 8 and write a sentence describing what this value is in
the context of the temperature function.
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