Math Question
![The continuous function \( g \), consisting of two line segments and a parabola, is defined on the closed interval \( [-3,6] \), is shown. Let \( f \) be a function such that \( f(1)=e \) and \( f^{\prime}(x)=e^{x}(1 \) \( +x) \).
Part A: Complete the table with positive, negative, or 0 to describe \( g^{\prime} \) and \( g^{\prime \prime} \). Justify your answers. (3 points)
\begin{tabular}{|c|l|l|l|l|}
\hline\( x \) & \( -3 x \) & \( -2 x \) & \( 1 \times \) & \( 4 x \) \\
\hline\( g(x) \) & positive & positive & positive & positive \\
\hline\( g^{\prime}(x) \) & & & & \\
\hline\( g^{\prime \prime}(x) \) & & & \\
\hline
\end{tabular}](https://d3hlidq5bf9vg0.cloudfront.net/app-server-student/2022/4/26/b22eacdf-b8e1-4db7-9dc3-bcbd2af35a49.png "The continuous function \( g \), consisting of two line segments and a parabola, is defined on the closed interval \( [-3,6] \), is shown. Let \( f \) be a function such that \( f(1)=e \) and \( f^{\prime}(x)=e^{x}(1 \) \( +x) \).
Part A: Complete the table with positive, negative, or 0 to describe \( g^{\prime} \) and \( g^{\prime \prime} \). Justify your answers. (3 points)
\begin{tabular}{|c|l|l|l|l|}
\hline\( x \) & \( -3 x \) & \( -2 x \) & \( 1 \times \) & \( 4 x \) \\
\hline\( g(x) \) & positive & positive & positive & positive \\
\hline\( g^{\prime}(x) \) & & & & \\
\hline\( g^{\prime \prime}(x) \) & & & \\
\hline
\end{tabular}")
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