Question

Given the function h(x)=-x^2+10x+32 determine the average rate of change of the function over the interval 3≤x≤11

Answer 1

Answer:

The average rate of change is 4

Step-by-step 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:

`\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}`
`\begin{gathered} Average\text{ rate of change = }\frac{53\text{ - 21}}{11\text{ - 3}} \\ \\ Average\text{ rate of change = }(32)/(8) \\ \\ Average\text{ rate of change = 4} \end{gathered}`