Question

find the average rate of change for the given function.
f(x)=x^{2}+10x between x = 0 and x = 5
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, $a = 0$, $b = 5$, and $f(x)=x^{2}+10x$.

Step2: Calculate $f(5)$

Substitute $x = 5$ into $f(x)$: $f(5)=5^{2}+10\times5=25 + 50=75$.

Step3: Calculate $f(0)$

Substitute $x = 0$ into $f(x)$: $f(0)=0^{2}+10\times0 = 0$.

Step4: Calculate the average rate of change

Using the formula $\frac{f(5)-f(0)}{5 - 0}$, substitute $f(5)=75$ and $f(0)=0$: $\frac{75-0}{5-0}=\frac{75}{5}=15$.

Answer:

15