Given That the Quadratic Taylor Polynomial of F at (4 $p ( x , y ) = - 2 + x ^ { 2 } + y ^ { 2 } - 4 x + 12 y$

question 2

Essay

Given that the quadratic Taylor polynomial of f at (4, 5)is $p ( x , y ) = - 2 + x ^ { 2 } + y ^ { 2 } - 4 x + 12 y$ decide whether $( 4,5 )$ is a critical point.If so, identify what sort of critical point it is.

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Definitions:

Crust

The outermost layer of the Earth, consisting of solid rocks, and subdivided into the continental and oceanic crust.

Subduction Zone

A region of the Earth's crust where two tectonic plates converge, and one plate is forced below the other into the mantle.

Metamorphism

Metamorphism is the process by which the mineral composition and texture of a rock are transformed by heat, pressure, and chemical processes.

Fold and Thrust Belts

These are elongated areas of folding and thrust faulting typically associated with convergent plate boundaries, leading to the formation of mountains and ridges.