Answer:
The average rate of change is -3.
Step-by-step explanation:
Given : Function [tex]f(x)=-3x+79[/tex] over the interval 2 ≤ x ≤ 4.
To find : What is the average rate of change ?
Solution :
Function [tex]f(x)=-3x+79[/tex] over [2,4]
The rate of change is the slope of the line,
So, [tex]\text{Rate of change}=\frac{f(4)-f(2)}{4-2}[/tex]
[tex]f(4)=-3(4)+79[/tex]
[tex]f(4)=-12+79[/tex]
[tex]f(4)=67[/tex]
[tex]f(2)=-3(2)+79[/tex]
[tex]f(2)=-6+79[/tex]
[tex]f(2)=73[/tex]
Substitute,
[tex]\text{Rate of change}=\frac{67-73}{4-2}[/tex]
[tex]\text{Rate of change}=\frac{-6}{2}[/tex]
[tex]\text{Rate of change}=-3[/tex]
Therefore, The average rate of change is -3.
