Find the Critical Points of the Function $f ( x , y , z ) = ( x - 4 ) ^ { 2 } + ( 7 - y ) ^ { 2 } + ( z - 2 ) ^ { 2 }$

question 66

Multiple Choice

Find the critical points of the function $f ( x , y , z ) = ( x - 4 ) ^ { 2 } + ( 7 - y ) ^ { 2 } + ( z - 2 ) ^ { 2 }$ , and, from the form of the function, determine whether a relative maximum or a relative minimum occurs at each point.

• A)relative minimum at \(( - 4 , - 7 , - 2 )\)
• B)relative maximum at \(( - 4 , - 7 , - 2 )\)
• C)relative minimum at \(( 4,7,2 )\)
• D)relative maximum at \(( 4,7,2 )\)
• E)no relative extrema

---

Definitions:

Restore

To restore means to bring something back to its original condition or to retrieve lost data from a backup source.

Positioning

The act of placing or arranging objects or elements in specific locations or configurations on a page or screen.

Specific Location

Refers to a precise geographical spot, often defined by a specific set of coordinates or an address.

Document

A written, drawn, presented, or memorialized representation of thought, often consisting of text, graphics, and other multimedia elements.