Question

given the function $g(x) = x^2 - 10x + 18$, determine the average rate of change of the function over the interval $1 \leq x \leq 11$.

Explanation:

Step1: Find $g(1)$

Substitute $x=1$ into $g(x)$:
$g(1) = 1^2 - 10(1) + 18 = 1 - 10 + 18 = 9$

Step2: Find $g(11)$

Substitute $x=11$ into $g(x)$:
$g(11) = 11^2 - 10(11) + 18 = 121 - 110 + 18 = 29$

Step3: Apply average rate formula

Use $\frac{g(b)-g(a)}{b-a}$ for $[a,b]=[1,11]$:
$\frac{g(11)-g(1)}{11-1} = \frac{29-9}{10} = \frac{20}{10} = 2$

Answer:

$2$