Respuesta :
The average rate of change from x = -1 to x = 2 is 2
Solution:
Given function is:
f(x) = 2x - 1
We have to find the average rate of change from x = -1 to x = 2
The average rate of change is given as:
[tex]\text {Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]
The average rate of change from x = -1 to x = 2 is given by formula:
[tex]\text {Average rate of change}=\frac{f(2)-f(-1)}{2-(-1)}\\\\\text {Average rate of change}=\frac{f(2)-f(-1)}{3}[/tex]
Find f(2) and f( - 1)
Substitute x = 2 in given function
f(2) = 2(2) - 1 = 4 - 1 = 3
Substitute x = -1 in given function
f( - 1) = 2(-1) - 1 = -2 - 1 = -3
Substitute the values in above formula,
[tex]\text {Average rate of change}=\frac{3-(-3)}{3}=\frac{6}{3}=2[/tex]
Thus average rate of change from x = -1 to x = 2 is 2
