Question

Given the function h(x)=x^2-8x+8, determine the average rate of change of the function over the interval 2≤x≤9.

Answer 1

The rule of the average rate of a function f(x) on the interval [a, b] is

$R=\frac{f(b)-f(a)}{b-a}$

Since the given function is

$f(x)=x^2-8x+8,2\leq x\leq9$

Then put a = 2 and b = 9, then find f(2) and f(9), and substitute them in the rule above.

$\begin{gathered} f(2)=(2)^2-8(2)+8 \\ f(2)=4-16+8 \\ f(2)=-4 \end{gathered}$$\begin{gathered} f(9)=(9)^2-8(9)+8 \\ f(9)=81-72+8 \\ f(9)=17 \end{gathered}$

Substitute the values of a, b, f(a), and f(b) in the rule above

$\begin{gathered} R=\frac{17--4}{9-2} \\ \\ R=\frac{17+4}{7} \\ \\ R=\frac{21}{7} \\ \\ R=3 \end{gathered}$

The average rate of change on the given interval is 3