Question

How do you determine whether the function `F(x) = x + 1/x` is concave up or concave down and its intervals?

Answer 1

See explanation.

Explanation:

For `f(x) = x + 1/x`, we get `f'(x) = 1-1/x^2` and `f''(x) = 2/x^3` which is negative for `x <0` and positive for `x > 0`.

So the graph of `f` is concave down on `(-oo,0)` and concave up on (0,oo)#

There is no inflection point because the concavity changes at `x=0` which is not in the domain of `f`.