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 \(( \pm 4,0 )\)

---

Definitions:

Chemical Imbalance

A theory suggesting that mental health conditions are associated with changes in the brain's chemical systems.

Excessive Anxiety

A state of heightened worry, nervousness, or unease that is disproportionate to the actual likelihood or impact of the feared event or situation.

Method

A systematic way of doing something, especially in scientific research or problem-solving.

Concept

An abstract idea or a mental symbol.