Find the tangent vector $\mathbf { r } ^ { \prime }$ (t) of the function r (t) = $\left( t , \sqrt { t } , \frac { 1 } { 2 \sqrt { t } } \right)$ when t = $\frac { 1 } { 4 }$ .
A) $( 1,2,4)$

B) $( 1,2 , - 2)$
C)$( 1,1,4 )$
D) $( 1,1 , - 2 )$
E) $( 1,2 , - 4 )$
F) $(1,2,2 )$

G) $( 1,1 , - 4 )$

H) $( 1,1,2 )$

Question

Find the tangent vector $\mathbf { r } ^ { \prime }$ (t) of the function r (t) = $\left( t , \sqrt { t } , \frac { 1 } { 2 \sqrt { t } } \right)$ when t = $\frac { 1 } { 4 }$ .
A) $( 1,2,4)$ 
 
B) $( 1,2 , - 2)$ 
C)$( 1,1,4 )$ 
D) $( 1,1 , - 2 )$ 
E) $( 1,2 , - 4 )$
F) $(1,2,2 )$

G) $( 1,1 , - 4 )$

H) $( 1,1,2 )$

Quizplus · Accepted Answer

The derivative of $ r(t) = (t, \sqrt{t}, \frac{1}{2\sqrt{t}}) $ is $ r'(t) = (1, \frac{1}{2\sqrt{t}}, -\frac{1}{4t^{3/2}}) $. Evaluating at $ t = \frac{1}{4} $, we get $ r'(\frac{1}{4}) = (1, 1, -2) $.

Find the Tangent Vector r′\mathbf { r } ^ { \prime }r′

Find the Tangent Vector $\mathbf { r } ^ { \prime }$