Question

Describe how to determine the average rate of change between x = 3 and x = 5 for the function f(x) = 3x3 + 2. include the average rate of change in your answer.

Answer 1

Answer:

147

Step-by-step explanation:

$\displaystyle \frac{f(b)-f(a)}{b-a}\\ \\\frac{f(5)-f(3)}{5-3}\\ \\\frac{(3(5)^3+2)-(3(3)^3+2)}{2}\\ \\\frac{(3(125)+2)-(3(27)+2)}{2}\\ \\\frac{(375+2)-(81+2)}{2}\\ \\\frac{377-83}{2}\\ \\\frac{294}{2}\\ \\147$

Recall that if a function $f$ is continuous over the interval $[a,b]$, then its average rate of change is $\frac{f(b)-f(a)}{b-a}$.