Given the Table of Data About the Second Derivative of a Function

Multiple Choice

Given the table of data about the second derivative of a function f, which of the following types of a function could f be? Assume b > 0.The other constants can be positive or negative.
$\begin{array}{lcccc}x & 0 & 1 & 2 & 3 \\& 1 & -2 & -5 & -8 \\f^{\prime \prime}(x) & & & &\end{array}$

A) $a e^{b x}$
B) $e^{-x^{2} / b}$
C) a quadratic (i.e. $a x^{2}+b x+c$ )
D) a cubic (i.e. $c x^{3}+b x^{2}+c x+d$ )
E) $\sin (b x)$