Given:
The function is,
[tex]h\mleft(x\mright)=x^2-9x+26[/tex]To find:
The average rate of change over the interval
[tex]-10\leq x\leq-2[/tex]Explanation:
Using the formula,
[tex]Average\text{ rate of function}=\frac{f(b)-f(a)}{b-a}[/tex]Here,
[tex]\begin{gathered} a=-10 \\ b=-2 \end{gathered}[/tex]The average rate of the function becomes,
[tex]\begin{gathered} Average\text{ rate of function}=\frac{f(-2)-f(-10)}{-2-(-10)} \\ =\frac{(-2)^2-9(-2)+26-((-10)^2-9(-10)+26)}{-2+10} \\ =\frac{4+18+26-(100+90+26)}{8} \\ =\frac{48-216}{8} \\ =\frac{-168}{8} \\ =-21 \end{gathered}[/tex]Therefore, the average rate of change of the function is -21.
Final answer:
The average rate of change of the function is -21.
