Question

Please help, thank you!

Answer 1

`y=-(1)/(5) x+2`

Explanation:

f(x) =
`(5)/(x)` ⇒ f(x) =
`5x^{-1`

Use the power rule to diferentiate:

f'(x) =
`-5x^{-2`

Plug in the value to differentiate at:

f'(5) =
`-5(5)^{-2` =
`-(1)/(5)` =
`m`

Plug into the equation of the tangent line:

`y-f(5)=f'(5)(x-5)`

`y=f'(5)(x-5)+f(5)`

`y=-(1)/(5) (x-5)+1`

`y=-(1)/(5) x+2`