# Thread: [SOLVED] Find the average rate of change

1. ## [SOLVED] Find the average rate of change

Find the average rate of change for: f(x) = x^2 - 3x + 5
a) [2 , 4]
b) [a , a + h]

2. $\displaystyle \frac{f(4) - f(2)}{4 - 2}$

$\displaystyle \frac{f(a+h) - f(a)}{(a+h) - a}$

work them out.

3. For a) I have: -8

For b) I have: h^2 + 2ah - 6a + 3h - 10 / 2

Is this correct?

4. $\displaystyle f(4) = 4^2 - 3(4) + 5 = 9$

$\displaystyle f(2) = 2^2 - 3(2) + 5 = 3$

$\displaystyle \frac{f(4) - f(2)}{4 - 2} = \frac{9 - 3}{4 - 2} = \, ?$

$\displaystyle f(a+h) = (a+h)^2 - 3(a+h) + 5 = a^2 + 2ah + h^2 - 3a - 3h + 5$

$\displaystyle f(a) = a^2 - 3(a) + 5 = a^2 - 3a + 5$

$\displaystyle \frac{f(a+h) - f(a)}{(a+h) - a} = \frac{2ah + h^2 - 3h}{h} = \, ?$

5. Originally Posted by skeeter
$\displaystyle f(4) = 4^2 - 3(4) + 5 = 9$

$\displaystyle f(2) = 2^2 - 3(2) + 5 = 3$

$\displaystyle \frac{f(4) - f(2)}{4 - 2} = \frac{9 - 3}{4 - 2} = \, ?$

$\displaystyle f(a+h) = (a+h)^2 - 3(a+h) + 5 = a^2 + 2ah + h^2 - 3a - 3h + 5$

$\displaystyle f(a) = a^2 - 3(a) + 5 = a^2 - 3a + 5$

$\displaystyle \frac{f(a+h) - f(a)}{(a+h) - a} = \frac{2ah + h^2 - 3h}{h} = \, ?$