Question

what is the average rate of change from f(-9) to f(-2)?
`f(x) = \sqrt[3]{x + 10} - 2`Type the numerical value for your answer as a whole number, decimal, or fraction

Answer 1

Question:

Solution:

Let the following function:

`f(x)=(x+10)^{(1)/(3)}-2`

Notice that:

`f(x_1)=f(-9)=(-9+10)^{(1)/(3)}-2\text{ = -1}`

and

`f(x_2)=_{}f(-2)=(-2+10)^{(1)/(3)}-2\text{ = }0`

thus the average rate is given by the following formula:

`(f(x_2)-f(x_1))/(x_2-x_1)\text{ = }\frac{0-(-1)}{-2\text{ +9}}=\text{ }(1)/(7)`

then, the correct answer is:

`(1)/(7)`