Question

given the function $h(x) = x^2 - 6x + 6$, determine the average rate of change of the function over the interval $0 \leq x \leq 7$.

Explanation:

Step1: Define average rate of change formula

The average rate of change of a function $h(x)$ over $[a,b]$ is $\frac{h(b)-h(a)}{b-a}$.

Step2: Calculate $h(0)$

$h(0) = 0^2 - 6(0) + 6 = 6$

Step3: Calculate $h(7)$

$h(7) = 7^2 - 6(7) + 6 = 49 - 42 + 6 = 13$

Step4: Compute average rate of change

$\frac{h(7)-h(0)}{7-0} = \frac{13-6}{7} = \frac{7}{7} = 1$

Answer:

$1$