Answer
$Rate_{Change} = 48$
Work Step by Step
Average rate of change is expressed by the following equation:
$$Rate_{Change}=\frac{f(x_{2}) - f(x_{1})}{x_{2} - x_{1}}$$
Therefore, having the values of $x_{2}$ and $x_{1}$, all we need is to find the values of $f(x_{2})$ and $f(x_{1})$:
$f(x_{2}) = 3(10)^{2} - 5 = 3(100) - 5 = 300 - 5 = 295$
$f(x_{1}) = 3(6)^{2} - 5 = 3(36) - 5 = 108 - 5 = 103$
$$Rate_{Change} = \frac{295 - 103}{10 - 6} = \frac{192}{4} = 48$$
