Question

I need help with this question please

Answer 1

-
`(1)/(12)`

Explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

`(f(b)-f(a))/(b-a)`

Here [ a, b ] = [ - 1, 3 ] , then

f(3) =
`(1)/(3-5)` = -
`(1)/(2)`

f(- 1) =
`(1)/(-1-5)` = -
`(1)/(6)`

average rate of change

=
`(-(1)/(2)-(-(1)/(6)) )/(3-(-1))`

=
`(-(1)/(2)+(1)/(6) )/(3+1)`

=
`(-(1)/(3) )/(4)`

= -
`(1)/(12)`

Answer 2

Average rate of change is - 1/6 or -0.166…

Explanation:

`{ \tt{f(x) = (1)/(x - 5) }}`

f(-1):

`{ \tt{f( - 1) = (1)/(( - 1 - 5)) }} \\ = { \tt{ - (1)/(6) }}`

f(3):

`{ \tt{f(3) = (1)/(3 - 5) }} \\ = { \tt{ - (1)/(2) }}`

Average rate of change:

`= { \bf{ (f(3) - f(-1))/(2) }}`

`{ \tt{ = ( - (1)/(2) - ( - (1)/(6) ) )/( 2 ) }} \\ \\ = { \tt{ - (1)/(6) }}`