Describe the Level Surfaces of the Function $f ( x , y , z ) = z - x ^ { 2 } - y ^ { 2 }$

question 175

Essay

Describe the level surfaces of the function $f ( x , y , z ) = z - x ^ { 2 } - y ^ { 2 }$ .

---

Definitions:

Single Seed

Refers to plants or fruits that produce or contain only one seed, distinguishing them from those that have multiple seeds.

Achene

A simple, dry fruit with one seed in which the fruit wall is separate from the seed coat (e.g., sunflower fruit).

Seed Coat Fused

A condition in some seeds where the outer protective layer, the seed coat, is naturally joined or united with other parts of the seed.

Large

A term used to describe something of significant size or extent in comparison to objects of the same category.