Find All the Local Maxima, Local Minima, and Saddle Points $$f ( x , y ) = x ^ { 2 } + 7 x y + y ^ { 2 }$$

question 402

Multiple Choice

Find all the local maxima, local minima, and saddle points of the function.
- $$f ( x , y ) = x ^ { 2 } + 7 x y + y ^ { 2 }$$

• A) f(7, 7) = 441, local maximim
• B) f(7, 0) = 49, local minimum; f(0, 7) = 49, local minimum
• C) f(0, 0) = 0, saddle point; f(7, 7) = 441, local maximim
• D) f(0, 0) = 0, saddle point

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Definitions:

Probability

A value between 0 and 1 determining how likely an event is to occur, representing its probability.

Uniform Density

Refers to a probability distribution where all outcomes are equally likely within a certain range.

Probability

A statistical measure that quantifies the likelihood of a specific event occurring within a set of conditions or experiments.

Normal Model

A statistical model based on the Normal (or Gaussian) distribution, characterized by a symmetrical bell-shaped curve indicating data dispersion.