Determine the average rate of change of the function on the given interval.
-$$f ( x ) = 3 x ^ { 2 } + 3 \text { on } [ 3,5 ]$$
A) $- 24$
B) $\frac { 5 } { 2 }$
C) 24
D) $\frac { 3 } { 2 }$

Question

Quizplus · Accepted Answer

The average rate of change of a function $f(x)$ on an interval $[a, b]$ is given by $\frac{f(b) - f(a)}{b - a}$. For $f(x) = 3x^2 + 3$ on $[3, 5]$, we calculate $f(5) = 3(5)^2 + 3 = 78$ and $f(3) = 3(3)^2 + 3 = 30$. Thus, the average rate of change is $\frac{78 - 30}{5 - 3} = \frac{48}{2} = 24$.

Determine the Average Rate of Change of the Function on the Given