Question

What is the average rate of change in f(x) over the interval [4,13]?


Group of answer choices

One-third

Eleven-eighths

Eleven-thirteenths

Four-thirteenths

Answer 1

The average rate of change = (change in the value on the y-axis) ÷ (the change in the value on the x-axis)

∴ $A = \frac{[f(b) - f(a)]}{(b - a)}$

Now, as given in the question,

a = 4

b = 13

f(a) = f(4) = 8

f(b) = f(13) = 11

On substituting these values with the corresponding parameters, we get;

$A = \frac{(11-8)}{(13-4)}$

⇒ $A = \frac{3}{9}$

⇒ $A = \frac{1}{3}$ (reducing the fraction to lowest terms)

Therefore, The average rate of change in f(x) over the interval (4, 13) is $(\frac{1}{3})$

Ans) (a) $(\frac{1}{3})$

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Answer 2

Thus the value of  average rate of change is 1/3.

Option (A) is correct.

Step-by-step explanation:

Average rate of change = change in value on y-axis ÷ Change in value on x-axis

A = [f (b) - f (a) ] / ( b - a)

We are given that:

a = 4 , b = 13

Now f (a) = f (4) = 8

f (b) = f (13) = 11

Now substitute the values.

A = ( 11 - 8) / ( 13 - 4)

A = 3 / 9 = 1 / 3

Thus the value of average rate of change is 1/3.