Suppose $\displaystyle {f}{''}{\left({x}\right)}$ is continuous for all $\displaystyle {x}$, and the graph of $\displaystyle {y}={f{{\left({x}\right)}}}$ has an inflection point at $\displaystyle {x}={9}$.

Complete the following table with appropriate possibilities for the values of $\displaystyle {f}{''}{\left({x}\right)}$ at $\displaystyle {x}={1},{9},{12}$..

$\displaystyle {x}$	$\displaystyle {1}$	$\displaystyle {9}$	$\displaystyle {12}$
$\displaystyle {f}{''}{\left({x}\right)}$

Based on your table, the graph of $\displaystyle {y}={f{{\left({x}\right)}}}$ is Select an answer concave up concave down until $\displaystyle {x}={9}$, and is Select an answer concave up concave down after.

The graph of $\displaystyle {y}={f{{\left({x}\right)}}}$ will have a Select an answer local maximum local minimum inflection point at $\displaystyle {x}={9}$.