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:

$f(x)=(x+10)^{\frac{1}{3}}-2$

Notice that:

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

and

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

thus the average rate is given by the following formula:

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

then, the correct answer is:

$\frac{1}{7}$