$\text { Locate the absolute extrema of the function } f ( x ) = \sin \pi x \text { on the closed interval }$

question 22

Multiple Choice

$\text { Locate the absolute extrema of the function } f ( x ) = \sin \pi x \text { on the closed interval }$ $\left[ 0 , \frac { 1 } { 3 } \right]$

• A) The absolute minimum is 0 , and it occurs at the left endpoint \(x = 0\). The absolute maximum is \(\frac { \sqrt { 3 } } { 2 }\), and it occurs at the right endpoint \(x = \frac { 1 } { 3 }\).
• B) The absolute minimum is 0 , and it occurs at the right endpoint \(x = \frac { 1 } { 3 }\).
• The absolute maximum is \(\frac { 1 } { 2 }\), and it occurs at the left endpoint \(x = 0\).
• C) The absolute minimum is 0 , and it occurs at the left endpoint \(x = 0\). The absolute maximum is \(\frac { 1 } { 2 }\), and it occurs at the right endpoint \(x = \frac { 1 } { 3 }\).
• D) The absolute minimum is 0 , and it occurs at the right endpoint \(x = \frac { 1 } { 3 }\).
• The absolute maximum is \(\frac { \sqrt { 2 } } { 2 }\) and it occurs at the left endpoint \(x = 0\).
• E) The absolute minimum is 0 , and it occurs at the left endpoint \(x = 0\).
• The absolute maximum is \(\frac { \sqrt { 2 } } { 2 }\), and it occurs at the right endpoint \(x = \frac { 1 } { 3 }\).

---

Definitions:

Uterine Tube

Also known as the fallopian tube, it is a part of the female reproductive system that connects the ovaries to the uterus, allowing the passage of eggs.

Uterus

A female reproductive organ where a fertilized egg implants and develops into a fetus; also known as the womb.

Vagina

A muscular and tubular part of the female genital tract, which extends from the vulva to the cervix and plays significant roles in intercourse, childbirth, and the passage of menstrual flow.

Ovary

A female reproductive organ in which ova or eggs are produced, present in pairs in the female reproductive system.