A Table of Values for a Function F near X $F ^ { \prime } ( 3 )$

question 47

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.Estimate $F ^ { \prime } ( 3 )$ using the right-hand estimate.
$$\begin{array} { c c c c } x & 2.9 & 3.0 & 3.1 \\F ( x ) & 6.7 & 7.0 & 7.3 \\G ( x ) & 5.2 & 5.0 & 4.8\end{array}$$ $\begin{array} { c c c c } \boldsymbol { x } & 6.9 & 7.0 & 7.1 \\G ( x ) & 0.95 & 1.00 & 1.05\end{array}$

---

Definitions:

Secondary Consumer

An animal that eats herbivores (primary consumers).

Primary Consumer

Herbivores that feed on primary producers (plants and algae), playing a pivotal role in the transfer of energy through the food chain.

Bird

A warm-blooded vertebrate characterized by feathers, beaks, and typically the ability to fly.

Primary Producer

Organisms, typically plants and algae, that produce organic compounds from carbon dioxide through photosynthesis, serving as a food source for other organisms in the ecosystem.