Provide an Appropriate Response $x = t , y = t ^ { 2 } , z = t$

Multiple Choice

Provide an appropriate response.
-For the space curve $x = t , y = t ^ { 2 } , z = t$ , find the points at which the function $f ( x , y )$ takes on extreme values if $f _ { X } =$ $9 , \mathrm { f } _ { \mathrm { y } } = \frac { \mathrm { t } } { 2 }$ , and $\mathrm { f } _ { \mathrm { z } } = - 30 \mathrm { t }$

A) $t = 0$
B) $t = \frac { 3 } { 2 }$ and $t = - \frac { 5 } { 2 }$
C) $t = 3$ and $t = - 5$
D) $t = 6$ and $t = - 10$