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)6y=f(x)nilebobo4oslon on bsismiggs S+(1, 2)mvolgmeanoisupsdgidmo bongrsdr ganob i(5,2)26orit 2s100 2 ups3450x

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Description: 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

Answered: Find the average rate of change of y…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 92E

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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

Expert Solution

Step 1

Formula used:

The average rate of change of the function $f (x)$ in the interval $(a, a + h)$ is

$A = \frac{f (a + h) - f (a)}{h}$ …(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,

$\begin{array}{rcl} a & = & 1 \\ h & = & 2 \end{array}$

Substitute $\begin{array}{rcl} a & = & 1 and h = 2 \end{array}$ in equation (1).

$\begin{array}{rcl} A & = & \frac{f (1 + 2) - f (1)}{2} \\ = & \frac{f (3) - f (1)}{2} \end{array}$

It is observed form the graph that $f (1) = 2$ and $f (3) = 6$ .

Substitute $f (1) = 2$ and $f (3) = 6$ in above equation.

$\begin{array}{rcl} A & = & \frac{6 - 2}{2} \\ = & \frac{4}{2} \\ = & 2 \end{array}$

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

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