Question

what is the average rate of change of $f(x)=7x$ over $0,5$?
a. 5
b. 7
c. 3
d. 2

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\).

Step2: Identify \(a\), \(b\), \(f(a)\) and \(f(b)\)

Here, \(a = 0\), \(b=5\), \(f(x)=7x\). So \(f(0)=7\times0 = 0\) and \(f(5)=7\times5=35\).

Step3: Substitute into the formula

\(\frac{f(5)-f(0)}{5 - 0}=\frac{35 - 0}{5}=\frac{35}{5}=7\)

Answer:

b. 7