Answer
$\text{average rate of change} =18$
Work Step by Step
The average rate of change of a function from $x=a$ to $x=b$ is given by the formula:
$\text{average rate of change} = \dfrac{f(b)-f(a)}{b-a}$
Use the formula above to obtain:
$$
\\= \dfrac{f(4)-f(2)}{4-a}
\\=\dfrac{(3\cdot4^2-2)-(3\cdot 2^2-2)}{4-2}
\\=\dfrac{(3\cdot16-2)-(3\cdot 4-2)}{2}
\\=\dfrac{(48-2)-(12-2)}{2}
\\=\dfrac{46-10}{2}
\\=\dfrac{36}{2}
\\=18$$
