Question

question
find the average rate of change of the given function on the interval 1,6.
g(x) = 2x² - x
select the correct answer below:
o 15
o 16
o 13
o 11
o 12

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = g(x)\) on the interval \([a,b]\) is \(\frac{g(b)-g(a)}{b - a}\). Here \(a = 1\), \(b=6\).

Step2: Calculate \(g(1)\) and \(g(6)\)

• For \(x = 1\): \(g(1)=2\times(1)^{2}-1=2 - 1=1\).
• For \(x = 6\): \(g(6)=2\times(6)^{2}-6=2\times36-6=72 - 6 = 66\).

Step3: Substitute into the formula

\(\frac{g(6)-g(1)}{6 - 1}=\frac{66 - 1}{5}=\frac{65}{5}=13\).

Answer:

13