7. if ( f(x)=6 x^{2}+3 x ), what is the average rate of change over (1,3)?\na. 27\nb. 30\nc. 18\nd. 36
7. if ( f(x)=6 x^{2}+3 x ), what is the average rate of change over (1,3)?\na. 27\nb. 30\nc. 18\nd. 36
Answer
Explanation:
Step1: Recall the formula for average rate of change
The formula for 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)) and (f(1))
- For (x = 3): (f(3)=6\times3^{2}+3\times3=6\times9 + 9=54 + 9=63)
- For (x = 1): (f(1)=6\times1^{2}+3\times1=6+3 = 9)
Step3: Substitute into the average - rate - of - change formula
(\frac{f(3)-f(1)}{3 - 1}=\frac{63 - 9}{2}=\frac{54}{2}=27)
Answer:
a. 27