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:

Straight-Line Method

A depreciation method that allocates an equal amount of the depreciable cost of an asset to each year of the asset's useful life.

Book Value

The value of an asset according to its balance sheet account balance, taking into account the cost of the asset minus depreciation.

Depreciation

is an accounting method that allocates the cost of a tangible asset over its useful life, reflecting the asset's consumption, wear and tear, or obsolescence.

Double-Declining-Balance Rate

A method of accelerated depreciation that doubles the rate at which an asset's value is reduced, resulting in higher depreciation expenses in the initial years of the asset's life.