Answer:
The average rate of change of the function [tex]f(x)=x^2-2x-5[/tex] for interval [tex]-5\leq x\leq 6[/tex] is -1
Step-by-step explanation:
We are given function [tex]f(x)=x^2-2x-5[/tex] and we need to determine the average rate of change of the function for interval [tex]-5\leq x\leq 6[/tex]
The formula used to find average rate of change is: [tex]Average \ rate \ of \ change=\frac{f(b)-f(a)}{b-a}[/tex]
We are given b=6 and a=-5
We need to find f(b) and f(a)
Finding f(b)
Putting x= 6 to find f(b)
[tex]f(x)=x^2-2x-5\\Put \ x=6\\f(6)=(6)^2-2(6)-5\\f(6)=36-12-5\\f(6)=19[/tex]
So, f(b)=19
Now finding f(a)
Putting x= -5 to find f(a)
[tex]f(x)=x^2-2x-5\\Put \ x=-5\\f(-5)=(-5)^2-2(-5)-5\\f(-5)=25+10-5\\f(-5)=30[/tex]
So, f(a)= 30
Finding average rate of change
[tex]Average \ rate \ of \ change=\frac{f(b)-f(a)}{b-a}\\Average \ rate \ of \ change=\frac{19-30}{6-(-5)}\\Average \ rate \ of \ change=\frac{-11}{6+5}\\Average \ rate \ of \ change=\frac{-11}{11}\\Average \ rate \ of \ change=-1[/tex]
Average rate of change = -1
So, average rate of change of the function [tex]f(x)=x^2-2x-5[/tex] for interval [tex]-5\leq x\leq 6[/tex] is -1
