Question

given the function h(x) = -x^2 - 9x + 23, determine the average rate of change the function over the interval -8 ≤ x ≤ 0

Answer 1

We are given the following function:

`h\mleft(x\mright)=-x^2-9x+23`

We are asked to determine the rate of change of the function in the interval:

`-8≤x≤0`

To do that we will use the following formula:

`r=(f(b)-f(a))/(b-a)`

Where "a" and "b" are the extreme values of the function. -

We have that "a = -8" and "b = 0". Now, we substitute the value of "a" in the function:

`\begin{gathered} f(-8)=-(-8)^2-9(-8)+23 \\ \\ f(-8)=31 \end{gathered}`

Now, we substitute the value of "b":

`\begin{gathered} f(0)=-(0)^2-9(0)+23 \\ \\ f(0)=23 \end{gathered}`

Now, we substitute the values in the formula for the rate of change:

`r=(23-31)/(0-(-8))=-1`

Therefore, the rate of change is -1