Find the Critical Points Of $f ( x , y ) = x ^ { 3 } - 9 x y + y ^ { 2 }$

question 49

Essay

Find the critical points of $f ( x , y ) = x ^ { 3 } - 9 x y + y ^ { 2 }$ and classify each as maximum, minimum or saddle.

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Definitions:

Cerebellar White Matter

The white neural tissue inside the cerebellum that contains myelinated nerve fibers connecting different parts of the cerebellum.

Primary Motor Cortex

The brain region located in the frontal lobe, responsible for the voluntary control of skeletal muscles.

Precentral Gyrus

A region of the cerebral cortex, located in the frontal lobe, responsible for motor control.

Cranial Nerves

Twelve pairs of nerves that emerge directly from the brain, not the spinal cord, and supply primarily the head and neck with motor and sensory innervation.