Question

functions over the start box. use your solution to move t ished! box. show your work for each ques
$f(x)=\frac{1}{2}x^{2}+2x-1$
$-2,4$
roc= ___

Explanation:

Step1: Define ROC formula

The rate of change (ROC) over interval $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$.

Step2: Calculate $f(4)$

$$\begin{align*} f(4)&=\frac{1}{2}(4)^2 + 2(4) - 1\\ &=\frac{1}{2}(16) + 8 - 1\\ &=8 + 8 - 1\\ &=15 \end{align*}$$

Step3: Calculate $f(-2)$

$$\begin{align*} f(-2)&=\frac{1}{2}(-2)^2 + 2(-2) - 1\\ &=\frac{1}{2}(4) - 4 - 1\\ &=2 - 4 - 1\\ &=-3 \end{align*}$$

Step4: Compute ROC

$$\begin{align*} \text{ROC}&=\frac{f(4)-f(-2)}{4-(-2)}\\ &=\frac{15 - (-3)}{6}\\ &=\frac{18}{6}\\ &=3 \end{align*}$$

Answer:

3