Question

find the average rate of change for the given function. f(x)=x^2 + 3x between x = 0 and x = 9 the average rate of change is . (simplify your answer.)

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 0$, $b = 9$, and $f(x)=x^{2}+3x$.

Step2: Calculate $f(9)$

Substitute $x = 9$ into $f(x)$: $f(9)=9^{2}+3\times9=81 + 27=108$.

Step3: Calculate $f(0)$

Substitute $x = 0$ into $f(x)$: $f(0)=0^{2}+3\times0 = 0$.

Step4: Calculate the average rate of change

Using the formula $\frac{f(9)-f(0)}{9 - 0}$, we substitute $f(9)=108$ and $f(0)=0$: $\frac{108-0}{9-0}=\frac{108}{9}=12$.

Answer:

12