Find the Extreme Values of the Function Subject to the Given

question 169

Multiple Choice

Find the extreme values of the function subject to the given constraint.
- $$f ( x , y ) = y ^ { 2 } - x ^ { 2 } , \quad x ^ { 2 } + y ^ { 2 } = 16$$

• A) Maximum: 32 at \(( 0 , \pm 4 \sqrt { 2 } )\); minimum: \(- 32\) at \(( \pm 4 \sqrt { 2 } , 0 )\)
• B) Maximum: 16 at \(( 0 , \pm 4 )\); minimum: \(- 32\) at \(( \pm 4 \sqrt { 2 } , 0 )\)
• C) Maximum: 32 at \(( 0 , \pm 4 \sqrt { 2 } )\); minimum: \(- 16\) at \(( \pm 4,0 )\)
• D) Maximum: 16 at \(( 0 , \pm 4 )\); minimum: \(- 16\) at \(( \pm 4,0 )\)

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Definitions:

Multiple Baseline Design

An experimental design used in behavioral research that introduces an intervention at different times across settings, behaviors, or individuals.

Line Graph

A type of chart used to display information as a series of data points connected by straight line segments, often used to visualize trends over time.

Key Parts

Essential components or elements that are crucial for the functionality or integrity of a whole.

Baseline

A reference point or starting level from which changes can be measured.