Question

Watch help videoGiven the function h(x) = x2 – 7x + 5, determine the average rate of change ofthe function over the interval –2 < x < 6.Answer:Submit Answerattempt 1 out of 2 / problem 1 out of max 1Privacy Policy Terms of ServiceCopyright 2021 DeltaMath.com. All Rights Reserved.

Answer 1

Let's write out the formula for average rate of change for the function,

$\begin{gathered} h(x)=\frac{h(b)-h(a)}{b-a},\text{ given the interval } \\ a\leq x\leq b \end{gathered}$$\begin{gathered} \text{where a=-2} \\ b=6 \\ \text{and the function of} \\ h(x)=x^2-7x+5 \end{gathered}$

Let us get h(x) when x=-2

$\begin{gathered} h(-2)=(-2)^2-7(-2)+5 \\ =4+14+5=23 \end{gathered}$

Let's get h(x) when x=6

$\begin{gathered} h(6)=(6)^2-7(6)+5 \\ =36-42+5=-1 \end{gathered}$$\begin{gathered} =\frac{h(6)-h(-2)}{6-(-2)} \\ =\frac{-1-23}{6-(-2)}=\frac{-24}{6+2} \\ =\frac{-24}{8}=-3 \end{gathered}$

Hence, the average rate of change of the function over the given interval is -3.