calculate the average rate of change of the function f(x) = 3x² over the interval 1 ≤ x ≤ 5. a 4 b 18 c 36 d…

Explanation:

Step1: Find function values at endpoints

First, find $f(1)$ and $f(5)$. For $x = 1$, $f(1)=3\times1^{2}=3$. For $x = 5$, $f(5)=3\times5^{2}=3\times25 = 75$.

Step2: Apply average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 1$, $b = 5$, $f(1)=3$, and $f(5)=75$. So, $\frac{f(5)-f(1)}{5 - 1}=\frac{75 - 3}{4}=\frac{72}{4}=18$.

Answer:

B. 18