Answer
a.)2
b.)0
Work Step by Step
The average rate of change of y = f(x) with respect to x over the interval [x1,x2] is:
$\frac{f(x2) - f(x1)}{x2-x1}$.
a.) g(x) = $x^{2}$ - 2x
Interval = [1,3]
$\frac{g(3) - g(1)}{3-1}$.
g(3) = $x^{2}$ -2x = $3^{2}$ -2.3 = 9-6 = 3
g(1) = $x^{2}$ -2x = $1^{2}$ -2.1= 1-2= -1
$\frac{3 - (-1)}{3-1}$. = $\frac{4}{2}$ = 2
b.)Interval = [-2, 4]
$\frac{g(4) - g(-2)}{4-(-2)}$.
g(4) = $x^{2}$ -2x = $4^{2}$ -2.4 = 16-8= 8
g(1) = $x^{2}$ -2x = $(-2)^{2}$ -2.(-2)= 4+4= 8
$\frac{8 - (8)}{4-(-2)}$. = $\frac{0}{6}$ = 0
