Question

Is `f(x)=(x^2-2)/(x+1)` increasing or decreasing at `x=1`?

Answer 1

It is increasing at `x=1`

Explanation:

You first need the derivative of `f`.

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

You now calculate it at `x=1` : `f'(1) = 5/4 > 0`.