Find All the Local Maxima, Local Minima, and Saddle Points $$f ( x , y ) = \left( x ^ { 2 } - 9 \right) ^ { 2 } + \left( y ^ { 2 } - 16 \right) ^ { 2 }$$

question 176

Multiple Choice

Find all the local maxima, local minima, and saddle points of the function.
- $$f ( x , y ) = \left( x ^ { 2 } - 9 \right) ^ { 2 } + \left( y ^ { 2 } - 16 \right) ^ { 2 }$$

• A) f(0, 0) = 337, local maximum; f(-3, -4) = 0, local minimum
• B) f(0, 0) = 337, local maximum; f(0, 4) = 81, saddle point; f(3, 0) = 256, saddle point; f(3, 4) = 0, local minimum; f(-3, -4) = 0, local minimum
• C) f(0, 0) = 337, local maximum; f(0, 4) = 81, saddle point; f(0, -4) = 81, saddle point; f(3, 0) = 337, saddle point; f(3, 4) = 0, local minimum; f(3, -4) = 0, local minimum;
• F(-3, 0) = 256, saddle point; f(-3, 4) = 0, local minimum; f(-3, -4) = 0, local minimum
• D) f(0, 0) = 337, local maximum; f(3, 4) = 0, local minimum; f(3, -4) = 0, local minimum; f(-3, 4) = 0, local minimum; f(-3, -4) = 0, local minimum

Recognize the significance of self-awareness in human psychological functioning.

Define and differentiate key existentialist and humanistic psychology terms.

Explain the process and criteria for achieving free will and authentic existence according to humanistic psychologists.

Understand the existential perspective on individual existence and experience.

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Definitions:

Variables

Elements, features, or factors that are likely to change or vary within the context of a research study or scientific experiment.

Usage Tax

A tax imposed on specific goods and services that is usually proportionate to the level of consumption or use.

High Variation

Refers to a wide range of values or outcomes within a set of data, indicating significant differences or fluctuations.

Low Variation

The characteristic of data or a set of values where the differences between the values are minimal, showing consistency.