f(x)=x^3 - 9x what is the average rate of change of f over the interval 1,6?
f(x)=x^3 - 9x what is the average rate of change of f over the interval 1,6?
Answer
Explanation:
Step1: Recall average - rate - of - change formula
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 $f(6)$
$f(6)=6^{3}-9\times6=216 - 54=162$.
Step3: Calculate $f(1)$
$f(1)=1^{3}-9\times1=1 - 9=-8$.
Step4: Calculate the average rate of change
$\frac{f(6)-f(1)}{6 - 1}=\frac{162-(-8)}{5}=\frac{162 + 8}{5}=\frac{170}{5}=34$.
Answer:
34