Question

Help with math question !!!

Answer 1

The average rate of change of the function
`f(x)=x^2-2x-5` for interval
`-5\leq x\leq 6` is -1

Explanation:

We are given function
`f(x)=x^2-2x-5` and we need to determine the average rate of change of the function for interval
`-5\leq x\leq 6`

The formula used to find average rate of change is:
`Average \ rate \ of \ change=(f(b)-f(a))/(b-a)`

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)

`f(x)=x^2-2x-5\\Put \ x=6\\f(6)=(6)^2-2(6)-5\\f(6)=36-12-5\\f(6)=19`

So, f(b)=19

Now finding f(a)

Putting x= -5 to find f(a)

`f(x)=x^2-2x-5\\Put \ x=-5\\f(-5)=(-5)^2-2(-5)-5\\f(-5)=25+10-5\\f(-5)=30`

So, f(a)= 30

Finding average rate of change

`Average \ rate \ of \ change=(f(b)-f(a))/(b-a)\\Average \ rate \ of \ change=(19-30)/(6-(-5))\\Average \ rate \ of \ change=(-11)/(6+5)\\Average \ rate \ of \ change=(-11)/(11)\\Average \ rate \ of \ change=-1`

Average rate of change = -1

So, average rate of change of the function
`f(x)=x^2-2x-5` for interval
`-5\leq x\leq 6` is -1