Question

question given the function ( h(x) = x^2 - 6x + 4 ), determine the average rate of change of the function over the interval ( -2 leq x leq 5 ). answer attempt 1 out of 3 submit answer

Explanation:

Step1: Recall the average rate of change formula

The average rate of change of a function \( h(x) \) over the interval \([a, b]\) is given by \(\frac{h(b) - h(a)}{b - a}\). Here, \( a=-2 \) and \( b = 5 \).

Step2: Calculate \( h(-2) \)

Substitute \( x=-2 \) into \( h(x)=x^{2}-6x + 4 \):
\[

$$\begin{align*} h(-2)&=(-2)^{2}-6(-2)+4\\ &=4 + 12+4\\ &=20 \end{align*}$$

\]

Step3: Calculate \( h(5) \)

Substitute \( x = 5 \) into \( h(x)=x^{2}-6x + 4 \):
\[

$$\begin{align*} h(5)&=5^{2}-6(5)+4\\ &=25-30 + 4\\ &=-1 \end{align*}$$

\]

Step4: Calculate the average rate of change

Using the formula \(\frac{h(5)-h(-2)}{5-(-2)}\), substitute \( h(5)=-1 \) and \( h(-2)=20 \):
\[

$$\begin{align*} \frac{h(5)-h(-2)}{5-(-2)}&=\frac{-1 - 20}{5 + 2}\\ &=\frac{-21}{7}\\ &=-3 \end{align*}$$

\]

Answer:

\(-3\)