Question

Find the average rate of change of f(x) = 2x ^ 2 - 9x from x = 2 to x = 5 . Simplify your answer as much as possible.

Answer 1

5

Explanation:

The average rate of change formula:

$\begin{gathered} \frac{\Delta y}{\Delta x}\text{ = }\frac{y2-y1}{x2-x1}\text{ = }\frac{f(b)\text{ -}f(a)}{b-a}\text{ } \\ \end{gathered}$$\begin{gathered} \frac{f(b)\text{f}(a)}{b-a}\text{ = }\frac{f(5)\text{ -f\lparen2\rparen}}{5-2} \\ \end{gathered}$$\begin{gathered} f(5)\text{ = 2*5}^2-9*5\text{ = 5} \\ f(2)\text{ = 2*2}^2-9*2\text{ = -10} \end{gathered}$$\frac{f(b)\text{f}(a)}{b-a}\text{ = }\frac{5-(-10)}{5-2}\text{ = }\frac{15}{3}\text{ = 5}$