Question

find the average rate of change of f(x)=2x^2+3x - 1 from 1 to 2.

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, $a = 1$, $b = 2$, and $f(x)=2x^{2}+3x - 1$.

Step2: Calculate $f(1)$

Substitute $x = 1$ into $f(x)$: $f(1)=2(1)^{2}+3(1)-1=2 + 3-1=4$.

Step3: Calculate $f(2)$

Substitute $x = 2$ into $f(x)$: $f(2)=2(2)^{2}+3(2)-1=2\times4 + 6-1=8 + 6-1=13$.

Step4: Calculate the average rate of change

Using the formula $\frac{f(b)-f(a)}{b - a}$, we have $\frac{f(2)-f(1)}{2 - 1}=\frac{13 - 4}{1}=9$.

Answer:

9