Question

What is the equation of the line tangent to `f(x)=(x^3 - 4) / x` at `x=2`?

Answer 1

`y-2=5(x-2)`
`y-2=5x-10`
`y=5x-8`

Explanation:

`f(x)=x^3/x -4/x`
`f(x)=x^2-4x^-1`
`f'(x)=2x+4/x^2`
`f'(2)=4+1=5`
`f(2)=(2^3-4)/2 = 4/2 = 2`
`y-2=5(x-2)`
`y-2=5x-10`
`y=5x-8`