Question

find the average rate of change of $f(x)=3x^2 + 2$ from $x = 2$ to $x = 4$. simplify your answer as much as possible.

Explanation:

Step1: Recall average rate formula

The average rate of change of $f(x)$ from $x=a$ to $x=b$ is $\frac{f(b)-f(a)}{b-a}$

Step2: Calculate $f(4)$

$f(4)=3(4)^2 + 2 = 3(16)+2=48+2=50$

Step3: Calculate $f(2)$

$f(2)=3(2)^2 + 2 = 3(4)+2=12+2=14$

Step4: Compute rate of change

$\frac{f(4)-f(2)}{4-2}=\frac{50-14}{2}=\frac{36}{2}=18$

Answer:

18