Answer
a)19
b)1
Work Step by Step
a.) The definition of average rate of change is
$\frac{f(x2) - f(x1)}{x2-x1}$.
Our interval is [2,3],
Now we put these into the function, and compute the values and we simply subtract them on the bottom of the fraction.
$\frac{f(3) - f(2)}{3-2}$.
f(3) = $x^{3}$ +1 = $3^{3}$ +1 = 28
f(2) = $x^{3}$ +1 = $2^{3}$ +1 = 9
$\frac{28- 9}{3-2}$. = 19
b.)
The definition of average rate of change is
$\frac{f(x2) - f(x1)}{x2-x1}$.
Our interval is [-1,1],
Now we put these into the function, and compute the values and we simply subtract them on the bottom of the fraction.
$\frac{f(1) - f(-1)}{1-(-1)}$.
f(1) = $x^{3}$ +1 = $1^{3}$ +1 = 2
f(-1) = $x^{3}$ +1 = $(-1)^{3}$ +1 = 0
$\frac{2- 0}{1+1}$. = 1
