OUESTION 2
The figure represents the graph of \( f(x)=-x^{3}+a x^{2}+b x+c \).
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\hline 2.1 & Show that \( a=5, b=8, c=-2 \). & (3) \\
\hline 2.2 & Determine the coordinates of the turning point A. & (4) \\
\hline 2.3 & Determine the equation of the tangent to \( f(x) \), where \( x=2 \) & (3) \\
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\hline 2.4 & Determine the values of \( x \) for which \( x . f^{\prime}(x) \geq 0 \). & (3) \\
\hline 2.5 & \begin{tabular}{l}
If \( f^{\prime}(x)=g^{\prime}(x) \) and \\
\( f(0)=g(0)-12 \), draw a sketch graph of \( g \). \\
Show the intercept on the \( y \)-axis and the turning point \( A \).
\end{tabular} & (4) \\
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