32. if f(x)=6x² + 3x, what is the average rate of change over 1,3? a. 27 b. 18 c. 30 d. 36

Answer:

A. 27

Explanation:

Step1: Recall 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, $a = 1$, $b = 3$, and $f(x)=6x^{2}+3x$.

Step2: Calculate $f(3)$

Substitute $x = 3$ into $f(x)$: $f(3)=6\times3^{2}+3\times3=6\times9 + 9=54 + 9=63$.

Step3: Calculate $f(1)$

Substitute $x = 1$ into $f(x)$: $f(1)=6\times1^{2}+3\times1=6 + 3=9$.

Step4: Calculate average rate of change

$\frac{f(3)-f(1)}{3 - 1}=\frac{63 - 9}{2}=\frac{54}{2}=27$.