Question

What is the equation of the line tangent to `f(x)=(x^3 - 1) / x` at `x=1`?

Answer 1

At `x=1`, we have `y = f(1) = 0` So the tangent line contains the point `(1,0)`

To find the slope, use

`f'(x) = ((3x^2)(x) - (x^3-1)(1))/x^2 = (2x^2 + 1)/x^2`

At `x=1`, the slope of the tangent is `f'(1) = 3`.

The equation of the tangent line sought is `y=3x-3`