Question

What is the average rate of change of the function over the interval [0,2]?LD12,4512010,5)11.15)-22A 15O B. 20C. 45D. 7.5

Answer 1

Points on the curve given below can be denoted as,

`\begin{gathered} (x_2,y_2)=(2,45) \\ (x_1,y_1)=(1,15) \end{gathered}`

`\begin{gathered} \text{Where,} \\ \text{slope m =}\frac{y_2-y_{1_{}}}{x_2-x_1} \end{gathered}`

Substituting the variables into the equation,

`\begin{gathered} m=(45-15)/(2-1)=(30)/(1)=30 \\ m=30 \end{gathered}`

To find the average rate change of the function over (0,2),

`\text{Average rate change =}\frac{\text{Slope}}{b-a}`

`\begin{gathered} (a,b)=(0,2) \\ \text{Average rate change=}(30)/(2-0)=(30)/(2)=15 \end{gathered}`

Hence, the average rate change of the function over the interval (0,2) is A "15".