F and G Are Functions Whose Graphs Are Shown Below $F ( x ) = f ( g ( x ) ) , G ( x ) = g ( f ( x ) )$

question 142

Essay

f and g are functions whose graphs are shown below. Let $F ( x ) = f ( g ( x ) ) , G ( x ) = g ( f ( x ) )$ and $H ( x ) = f ( f ( x ) )$ Find each derivative, if it exists. If it does not exist, explain. (a) $F ^ { \prime } ( 2 )$ (b) $F ^ { \prime } ( 6 )$ (c) $F ^ { \prime } ( 8 )$ (d) $G ^ { \prime } ( 2 )$ (e) $G ^ { \prime } ( 4 )$ (f) $G ^ { \prime } ( 10 )$ (g) $H ^ { \prime } ( 4 )$ (h) $H ^ { \prime } ( 6 )$ (i) $H ^ { \prime } ( 10 )$

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Definitions:

Arbitrage

Practice of buying at a low price at one location and selling at a higher price in another.

Convertible Bond

A type of bond that can be converted by the holder into a specified number of shares of the issuing company's stock at certain times during its life, usually at the discretion of the bondholder.

Acme Corporation

A fictional company often used as a generic placeholder in examples and discussions to represent any typical, large-scale business entity.

Ketone Bodies

Water-soluble molecules produced by the liver from fatty acids during periods of low food intake, carbohydrate restrictive diets, fasting, or prolonged intense exercise.