Question

1. find the average rate of change of f(x) over the interval 18, 24.

x | f(x)
12 | 41
18 | 40
24 | 39
30 | 38
working:
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, \( a = 18 \), \( b = 24 \), \( f(18)=40 \), and \( f(24) = 39 \).

Step2: Substitute the values into the formula

Substitute \( a = 18 \), \( b = 24 \), \( f(18) = 40 \), and \( f(24)=39 \) into the formula: \(\frac{f(24)-f(18)}{24 - 18}=\frac{39 - 40}{24 - 18}\).

Step3: Simplify the numerator and the denominator

First, calculate the numerator: \( 39-40=- 1 \). Then, calculate the denominator: \( 24 - 18 = 6 \). So the expression becomes \(\frac{-1}{6}\).

Answer:

\(-\frac{1}{6}\)