Find the average rate of change of y with respect to x (a) on the interval (1, 3), (b) on the interval (3, 5).

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 1SE: Can the average rate of change of a function be constant?
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I'm confused because f(x) doesn't have a rule so I'm unsure how to plug in the x and y values into the rate of change formula. f(a+h) - f(a) / h

9. Find the average rate of change of y with respect to x (a)
on the interval (1, 3), (b) on the interval (3, 5).
y A
(3,6)
6
y=f(x)nilebo
bo
4
oslon on bsismiggs S+
(1, 2)mvolgmean
oisups
dgid
mo bongrsdr ganob i
(5,2)
26
orit 2s
100 2 ups3
4
50x
Transcribed Image Text:9. Find the average rate of change of y with respect to x (a) on the interval (1, 3), (b) on the interval (3, 5). y A (3,6) 6 y=f(x)nilebo bo 4 oslon on bsismiggs S+ (1, 2)mvolgmean oisups dgid mo bongrsdr ganob i (5,2) 26 orit 2s 100 2 ups3 4 50x
Expert Solution
Step 1

Formula used:

The average rate of change of the function fx in the interval a,a+h is

A=fa+h-fah                                                                          …(1)

Here, A is rate of change of the function.

Calculation:

(a)

The interval 1,3 can be written in the form of a,a+h as,

1,3=1,1+2

Compare 1,1+2 with a,a+h to obtain the value of a and h as,

a=1h=2

Substitute a=1 and h=2 in equation (1).

A=f1+2-f12=f3-f12

It is observed form the graph that f1=2 and f3=6.

Substitute f1=2 and f3=6 in above equation.

A=6-22=42=2

Thus, the average rate of change of the function in the interval 1,3 is 2. 

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