A Table of Values for a Function F near X $H ( x ) = G ( F ( x ) )$

question 24

Short Answer

A table of values for a function F near x = 3 and tables of values for a function G near x = 3 and near x = 7 are given below.If $H ( x ) = G ( F ( x ) )$ , estimate H'(3)using the chain rule.Use right-hand estimates for $F ^ { \prime }$ and $G ^ { \prime }$ .
$$\begin{array} { c c c c } x & 2.9 & 3.0 & 3.1 \\F ( x ) & 6.7 & 7.0 & 7.3 \\G ( x ) & 5.2 & 5.0 & 4.8\end{array}$$ $$\begin{array} { c c c } x & 6.9 & 7.0&7.1 \\G ( x ) & 5.85 & 6.00&6.15\end{array}$$