Question

What is the equation of the line tangent to `f(x)=1/abs(x)` at `x=1`?

Answer 1

`y = -x + 2`

Explanation:

at `x = 1, abs x = x`

so

`f(x) = 1/x`
`f(1) = 1`
`f'(x) = - 1/x^2`
`f'(1) = -1`

`y - y_0 = m (x - x_o)`

`implies y - 1 = -1(x - 1)`

`y = -x + 2`