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

There are no inflection points for this $f$.
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.
$f \left(x\right) = x \sqrt{x + 1}$ has domain $\left[- 1 , \infty\right)$
$f ' ' \left(x\right) = \frac{3 x + 4}{4 {\left(x + 1\right)}^{\frac{3}{2}}}$ is positive on $\left(- 1 , \infty\right)$ so there are no inflection points for $f$.