Examine the Function $f ( x , y ) = 4 x ^ { 2 } - 2 x y + 4 y ^ { 2 } + 120 x + 60 y$

question 19

Multiple Choice

Examine the function $f ( x , y ) = 4 x ^ { 2 } - 2 x y + 4 y ^ { 2 } + 120 x + 60 y$ for relative extrema.

• A)relative \(\text { minimum }\) at \(( - 18 , - 12 )\)
• B)relative \(\text { maximum }\) at \(( - 18 , - 12 )\)
• C)relative \(\text { minimum }\) at \(( - 18,12 )\)
• D)relative \(\text { maximum }\) at \(( - 18,12 )\)
• E)no relative extrema

---

Definitions:

Pearson Correlation

A measure of the linear correlation between two variables, represented by a value between -1 and 1.

Null Hypothesis

Re-stated: The hypothesis that assumes no real effect, variance, or difference within the scope of the experimental and observational study parameters.

Covariance

A measure indicating the extent to which two random variables change in tandem.

Covariance

A measure that indicates the extent to which two variables change together, showing if increases in one variable correspond to increases or decreases in another.