Below Is a Table Containing Information About the Differentiable Functions

Essay

Below is a table containing information about the differentiable functions f and g. $$\begin{array} { | l | r | r | r | r | r | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline f ( x ) & 4 & 3 & 5 & 2 & 1 \\f ^ { \prime } ( x ) & 1 & 4 & 2 & 5 & 3 \\g ( x ) & 5 & 2 & 1 & 3 & 4 \\g ^ { \prime } ( x ) & 3 & 5 & 4 & 1 & 2 \\\hline\end{array}$$ Suppose also that $F ( x ) = f ( x ) + g ( x )$ , $G ( x ) = f ( x ) \cdot g ( x )$ , and $H ( x ) = \frac { g ( x ) } { f ( x ) }$ .(a) Find $F ^ { \prime } ( 0 )$ (b) Find $G ^ { \prime } ( - 2 )$ (c) Find $H ^ { \prime } ( 2 )$