Find All the Critical Points Of $f ( x , y ) = x ^ { 3 } - 3 x + y ^ { 2 } - 4 y$

question 10

Multiple Choice

Find all the critical points of $f ( x , y ) = x ^ { 3 } - 3 x + y ^ { 2 } - 4 y$ and classify each as maximum, minimum, or saddle point. Select all possible choices.

• A)The point (1, 2)is a relative minimum.
• B)The point (-1, -2)is a saddle point.
• C)The point (-1, 2)is a saddle point.
• D)The point (1, 2)is a relative maximum.
• E)The point (1, -2)is a relative maximum.

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Definitions:

Sell Shares

The act of offloading equity stakes in a company, usually in the form of stock, to raise capital or realize gains from investment.

Exercise Price

The predetermined price at which the holder of an option can buy (call) or sell (put) the underlying asset or security.

Black-Scholes

A mathematical model used to determine the theoretical price of European-style options, factoring in time, volatility, interest rates, and dividend payments.

Intrinsic Value

The lower bound of an option’s value, or what the option would be worth if it were about to expire.