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

question 65

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) \(\sin (b x)\)

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