what is the average rate of change of the function f(x) = x² + 3x - 10 on the interval from x = 0 to x = 2?

Answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 0$, $b = 2$, and $f(x)=x^{2}+3x - 10$.

Step2: Calculate $f(2)$

Substitute $x = 2$ into $f(x)$: $f(2)=2^{2}+3\times2 - 10=4 + 6-10=0$.

Step3: Calculate $f(0)$

Substitute $x = 0$ into $f(x)$: $f(0)=0^{2}+3\times0 - 10=-10$.

Step4: Calculate the average rate of change

Using the formula $\frac{f(b)-f(a)}{b - a}$, we have $\frac{f(2)-f(0)}{2 - 0}=\frac{0-(-10)}{2}=\frac{10}{2}=5$.