Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 10 ≤ x ≤ 40.

x	f(x)
20	53
30	51
40	49
50	47
60	45

answer attempt 1 out of 2

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, \(a = 10\), \(b = 40\), \(f(10)=55\) and \(f(40) = 49\).

Step2: Substitute the values into the formula

Substitute \(a = 10\), \(b = 40\), \(f(a)=55\) and \(f(b)=49\) into the formula:

$$ \frac{f(40)-f(10)}{40 - 10}=\frac{49 - 55}{40-10} $$

Step3: Simplify the numerator and the denominator

First, simplify the numerator: \(49-55=- 6\)
Then, simplify the denominator: \(40 - 10=30\)
So we have \(\frac{-6}{30}\)

Step4: Reduce the fraction to its simplest form

Divide both the numerator and the denominator by their greatest common divisor, which is 6.
\(\frac{-6\div6}{30\div6}=\frac{- 1}{5}\)

Answer:

\(-\frac{1}{5}\)