Provide an Appropriate Response $\mathrm { f } ( \mathrm { x } , \mathrm { y } )$

question 278

Multiple Choice

Provide an appropriate response.
-Find any local extrema (maxima, minima, or saddle points) of $\mathrm { f } ( \mathrm { x } , \mathrm { y } )$ given that $\mathrm { f } _ { \mathrm { x } } = 5 \mathrm { x } + 5 \mathrm { y }$ and $\mathrm { f } _ { \mathrm { y } } = 3 \mathrm { x } - 8 \mathrm { y }$ .

• A) Local maximum at \(\left( - 1 , \frac { 8 } { 3 } \right)\)
• B) Saddle point at \(( - 40,15 )\)
• C) Saddle point at \(( 0,0 )\)
• D) Local minimum at \(\left( - 1 , \frac { 8 } { 3 } \right)\)

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Definitions:

Wilcoxon Test Statistic

A non-parametric test statistic used to compare two paired samples to assess whether their population mean ranks differ.

Null Hypothesis

A hypothesis that assumes no statistical significance or effect exists in a set of observations.

Level Of Significance

The threshold below which a statistical result is considered significant, indicating that an observed effect is unlikely to be due to chance alone.

Quantitative Data

Data that can be quantified and verified, and is amenable to statistical manipulation, typically involving numerical values.