Question

find average rate of change from table
question
given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval ( 3 leq x leq 4 ).

( x )	( f(x) )
3	31
4	22
5	15
6	10

answer

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( f(x) \) over the interval \( [a, b] \) is given by \( \frac{f(b) - f(a)}{b - a} \). Here, \( a = 3 \) and \( b = 4 \).

Step2: Find \( f(3) \) and \( f(4) \) from the table

From the table, when \( x = 3 \), \( f(3) = 31 \); when \( x = 4 \), \( f(4) = 22 \).

Step3: Substitute into the formula

Substitute \( a = 3 \), \( b = 4 \), \( f(3) = 31 \), and \( f(4) = 22 \) into the formula:
\[
\frac{f(4) - f(3)}{4 - 3} = \frac{22 - 31}{4 - 3}
\]

Step4: Simplify the expression

First, calculate the numerator: \( 22 - 31 = -9 \). The denominator is \( 4 - 3 = 1 \). So, \( \frac{-9}{1} = -9 \).

Answer:

\( -9 \)