Find the Local Maximum and Minimum Values and Saddle Points $f ( x , y ) = - x ^ { 4 } + 4 x y - 2 y ^ { 2 } + 1$

question 264

Essay

Find the local maximum and minimum values and saddle points of the function $f ( x , y ) = - x ^ { 4 } + 4 x y - 2 y ^ { 2 } + 1$ .

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Definitions:

Selling Price

The amount of money for which a product or service is sold to customers.

Face Value

The original cost of a bond or the principal balance to be paid back at maturity, excluding interest.

Market Interest Rate

The prevailing rate at which interest is charged on loans and bonds in the broader financial market.

Bond Yield

The return an investor realizes on a bond, calculated by the coupon payments relative to the market price of the bond.