The average rate of change is 4
Explanation:Given:
h(x) = -x²+ 10x + 32
The interval is 3≤x≤11
To find:
The rate of change for the given interval
To find the above, we will apply the formula for rate of change:
[tex]\begin{gathered} A(x)\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ h(x)\text{ = -x^^b2+ 10x + 32 } \\ A(x)\text{ = }\frac{h(x_2)\text{ - h\lparen x}_1)}{x_2-x_1} \end{gathered}[/tex][tex]\begin{gathered} interval\text{ is }3≤x≤11 \\ x_1\text{ = 3, x}_2\text{ = 11} \\ when\text{ x = 3} \\ h(x)\text{ = -\lparen3\rparen}^2\text{ + 10\lparen3\rparen + 32} \\ h(x)\text{ = 53} \\ \\ when\text{ x = 11} \\ h(x)\text{ = -\lparen11\rparen}^2\text{ + 10\lparen11\rparen + 32} \\ h(x)\text{ = 21} \end{gathered}[/tex][tex]\begin{gathered} Average\text{ rate of change = }\frac{53\text{ - 21}}{11\text{ - 3}} \\ \\ Average\text{ rate of change = }\frac{32}{8} \\ \\ Average\text{ rate of change = 4} \end{gathered}[/tex]