The function is given as,
[tex]h(x)\text{ = -x}^2+4x+11\text{ over the interval 0 }\leq\text{ x }\leq\text{ 6.}[/tex]
The average rate of change of the function over the interval x [a,b] is given by,
[tex]\frac{h(b)-h(a)}{b-a}[/tex]
The average rate of change of the function over the interval,
[tex]\begin{equation*} \text{ 0 }\leq\text{ x }\leq\text{ 6.} \end{equation*}[/tex]
is given by,
[tex]\frac{h(6)\text{ - h\lparen0\rparen}}{6-0}\text{ = }\frac{-1+11}{6}\text{ = }\frac{10}{6}\text{ = }\frac{5}{3}[/tex]
Thus the average rate of change is 5/3 or 1.67.
