Question

How do you find the points of inflection for `f(x)=x sqrt(x+1)`?

Answer 1

There are no inflection points for this `f`.

Explanation:

An inflection point is a point of the graph of `f` at which the concavity changes. It is a point on the graph at which the sign of `f''` changes.

`f(x) = xsqrt(x+1)` has domain `[-1,oo)`

`f''(x) = (3x+4)/(4(x+1)^(3/2))` is positive on `(-1,oo)` so there are no inflection points for `f`.