Question

AnOtHeR MATH QUESTION (SMH). HELP PLEASE !!!

Answer 1

For the function:
`g(x)=-x^2-3x+5`, the average rate of change of function over the interval
`-7\leq x\leq 2` is 2

Explanation:

We are given function:
`g(x)=-x^2-3x+5`, we need to find average rate of change of function over the interval
`-7\leq x\leq 2`

The formula used is:
`Average \ rate \ of \ change=(g(b)-g(a))/(b-a)`

We have b=2 and a= -7

Finding f(b) and f(a)

Finding g(b) by putting x=2

`g(x)=-x^2-3x+5\\g(2)=-(2)^2-3(2)+5\\g(2)=-4-6+5\\g(2)=-10+5\\g(2)=-5`

Finding g(a) by putting x=-7

`g(x)=-x^2-3x+5\\g(-7)=-(-7)^2-3(-7)+5\\g(-7)=-49+21+5\\g(-7)=-23`

Now, finding average rate of change when g(b)=-5 and g(a)=-23

`Average \ rate \ of \ change=(g(b)-g(a))/(b-a)\\Average \ rate \ of \ change=(-5-(-23))/(2-(-7))\\Average \ rate \ of \ change=(-5+23)/(2+7)\\Average \ rate \ of \ change=(18)/(9)\\Average \ rate \ of \ change=2`

So, Average rate of change = 2

Therefore for the function:
`g(x)=-x^2-3x+5`, the average rate of change of function over the interval
`-7\leq x\leq 2` is 2