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

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Answer 1 · 2015-10-22T22:48:32

See 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 $f$ .

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