Respuesta :
We are given the following function:
[tex]h\mleft(x\mright)=-x^2-9x+23[/tex]We are asked to determine the rate of change of the function in the interval:
[tex]-8≤x≤0[/tex]To do that we will use the following formula:
[tex]r=\frac{f(b)-f(a)}{b-a}[/tex]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:
[tex]\begin{gathered} f(-8)=-(-8)^2-9(-8)+23 \\ \\ f(-8)=31 \end{gathered}[/tex]Now, we substitute the value of "b":
[tex]\begin{gathered} f(0)=-(0)^2-9(0)+23 \\ \\ f(0)=23 \end{gathered}[/tex]Now, we substitute the values in the formula for the rate of change:
[tex]r=\frac{23-31}{0-(-8)}=-1[/tex]Therefore, the rate of change is -1
