Question

average rate of change of polynomials
google classroom
microsoft teams
you might need: calculator
what is the average rate of change of ( f ) over the interval ( 1,6 )?

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 \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 1\), \(b=6\), and \(f(x)=x^{3}-9x\).

Step2: Calculate \(f(6)\)

Substitute \(x = 6\) into \(f(x)\): \(f(6)=6^{3}-9\times6=216 - 54=162\).

Step3: Calculate \(f(1)\)

Substitute \(x = 1\) into \(f(x)\): \(f(1)=1^{3}-9\times1=1 - 9=-8\).

Step4: Calculate the average rate of change

Using the formula \(\frac{f(b)-f(a)}{b - a}\), substitute \(f(6)=162\), \(f(1)=-8\), \(a = 1\), and \(b = 6\): \(\frac{162-(-8)}{6 - 1}=\frac{162 + 8}{5}=\frac{170}{5}=34\).

Answer:

\(34\)