Answer the Problem $f ( x ) = \left| x ^ { 3 } - 9 x \right|$

question 408

Essay

Answer the problem.
-Let $f ( x ) = \left| x ^ { 3 } - 9 x \right|$
(a) Does $f ^ { \prime } ( 0 )$ exist?
(b) Does $\mathrm { f } ^ { \prime } ( 3 )$ exist?
(c) Does $f ^ { \prime } ( - 3 )$ exist?
(d) Determine all extrema of $f$ .

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Definitions:

Absolute Advantage

The ability of an entity to produce a good or service more efficiently than its competitors.

Comparative Advantage

An economic theory that describes how countries or individuals can gain by specializing in the production of goods and services for which they have a lower opportunity cost, leading to beneficial trade.

Absolute Advantage

The ability of a country or entity to produce a good more efficiently (using fewer resources) than another country or entity.

Specializing

The process of focusing on and becoming expert in a particular subject or skill.