find average rate of change from equation this is the only question in this section. question given the…

find average rate of change from equation this is the only question in this section. question given the function h(x)=x² - 6x + 6, determine the average rate of change of the function over the interval 0 ≤ x ≤ 7. answer attempt 1 out of 8

find average rate of change from equation this is the only question in this section. question given the function h(x)=x² - 6x + 6, determine the average rate of change of the function over the interval 0 ≤ x ≤ 7. answer attempt 1 out of 8

Answer

Explanation:

Step1: Definir la fórmula

La tasa promedio de cambio de una función $y = h(x)$ en el intervalo $[a,b]$ está dada por $\frac{h(b)-h(a)}{b - a}$. Aquí, $a = 0$, $b = 7$ y $h(x)=x^{2}-6x + 6$.

Step2: Calcular $h(7)$

Sustituir $x = 7$ en $h(x)$: $h(7)=7^{2}-6\times7 + 6=49-42 + 6=13$.

Step3: Calcular $h(0)$

Sustituir $x = 0$ en $h(x)$: $h(0)=0^{2}-6\times0 + 6=6$.

Step4: Calcular la tasa promedio de cambio

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

Answer:

$1$