Question

find the average rate of change of ( h(x) = x^2 - 5x + 1 ) from ( x = 4 ) to ( x = 6 ).
simplify your answer as much as possible.

Explanation:

Step1: Define average rate of change formula

The average rate of change of a function $h(x)$ from $x=a$ to $x=b$ is $\frac{h(b)-h(a)}{b-a}$.

Step2: Calculate $h(6)$

Substitute $x=6$ into $h(x)$:
$h(6) = 6^2 - 5(6) + 1 = 36 - 30 + 1 = 7$

Step3: Calculate $h(4)$

Substitute $x=4$ into $h(x)$:
$h(4) = 4^2 - 5(4) + 1 = 16 - 20 + 1 = -3$

Step4: Compute average rate of change

Substitute values into the formula:
$\frac{h(6)-h(4)}{6-4} = \frac{7 - (-3)}{2} = \frac{10}{2} = 5$

Answer:

5