If $f ( x ) = e ^ { x } g ( x ) \text {, and if } g ( 0 ) = 3 \text { and } g ^ { \prime } ( 0 ) = - 2 \text {, find } f ^ { \prime } ( 0 ) \text {. }$

question 172

Essay

If $f ( x ) = e ^ { x } g ( x ) \text {, and if } g ( 0 ) = 3 \text { and } g ^ { \prime } ( 0 ) = - 2 \text {, find } f ^ { \prime } ( 0 ) \text {. }$

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Definitions:

Laissez-faire

An economic philosophy of free-market capitalism that opposes government intervention.

Democratic

Pertaining to a form of government in which power is vested in the hands of the people, directly or through elected representatives.

Class Inequality

Disparities in access to resources, opportunities, and privileges among different social classes within a society, often stemming from economic disparities.

Horticultural Societies

Those in which people domesticate plants and use simple hand tools to garden. Such societies first emerged about 10,000 years ago. Horticulture increases the food supply and makes it more dependable. This increases average settlement size and permanence, the division of labor, productivity, and inequality above the levels typical of foraging societies.