Question

2.
find the average rate of change (in simplest form) on the interval 3;6.

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( f(x) \) on the interval \([a, b]\) is given by \(\frac{f(b) - f(a)}{b - a}\). Here, \( a = 3 \), \( b = 6 \), so we need to find \( f(3) \) and \( f(6) \).
From the table, \( f(3) = 24 \) and \( f(6) = 6 \).

Step2: Substitute into the formula

Substitute \( a = 3 \), \( b = 6 \), \( f(3) = 24 \), and \( f(6) = 6 \) into the formula:

$$ \frac{f(6) - f(3)}{6 - 3} = \frac{6 - 24}{6 - 3} $$

Step3: Simplify the numerator and denominator

First, calculate the numerator: \( 6 - 24 = -18 \).
Then, calculate the denominator: \( 6 - 3 = 3 \).
So we have \(\frac{-18}{3}\).

Step4: Simplify the fraction

\(\frac{-18}{3} = -6\).

Answer:

\(-6\)