Find the Extreme Values of the Function Subject to the Given

question 347

Multiple Choice

Find the extreme values of the function subject to the given constraint.
- $$f ( x , y , z ) = x + y + z , \frac { 1 } { x } + \frac { 1 } { y } + \frac { 1 } { z } = 1$$

• A) Maximum: 9 at (3, 3, 3); minimum: 3 at (1, 1, 1)
• B) Maximum: 11 at (6, 3, 2), (6, 2, 3), (3, 2, 6), (3, 6, 2), (2, 3, 6), (2, 6, 3); minimum: 1 at (1, 1, -1), (1, -1, 1), (-1, 1, 1)
• C) Maximum: 6 at (2, 2, 2); minimum: -3 at (-1, -1, -1)
• D) Maximum: 6 at (2, 2, 2); minimum: 3 at (1, 1, 1)

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Definitions:

Diaphragm

A dome-shaped, flexible barrier device inserted into the vagina to prevent pregnancy by covering the cervix.

Vagina

The muscular tube leading from the external genitals to the cervix of the uterus in women and most female mammals.

Last Intercourse

The most recent occasion on which an individual engaged in sexual activity with another person.

Female Condom

A barrier device used during sexual activity to reduce the risk of sexually transmitted infections (STIs) and pregnancy by covering the inside of the vagina.