Find the slope of the tangent line to the graph of the given function at the indicated point. $g ( t ) = \frac { 8 } { t ^ { 3 } } , ( 1.5,57 )$
A) $g ^ { \prime } ( 1.5 ) = - 108$
B) $g ^ { \prime } ( 1.5 ) = - 36$
C) $g ^ { \prime } ( 1.5 ) = 54$
D) $g ^ { \prime } ( 1.5 ) = - 27$
E) $g ^ { \prime } ( 1.5 ) = - 54$

Question

Find the slope of the tangent line to the graph of the given function at the indicated point.   $g ( t ) = \frac { 8 } { t ^ { 3 } } , ( 1.5,57 )$  
A) $g ^ { \prime } ( 1.5 ) = - 108$
B) $g ^ { \prime } ( 1.5 ) = - 36$
C) $g ^ { \prime } ( 1.5 ) = 54$
D) $g ^ { \prime } ( 1.5 ) = - 27$
E) $g ^ { \prime } ( 1.5 ) = - 54$

Quizplus · Accepted Answer

The derivative of $g(t) = \frac{8}{t^3}$ is $g'(t) = -\frac{24}{t^4}$. Evaluating at $t = 1.5$, we get $g'(1.5) = -\frac{24}{(1.5)^4} = -54$.

Find the Slope of the Tangent Line to the Graph g(t)=8t3,(1.5,57)g ( t ) = \frac { 8 } { t ^ { 3 } } , ( 1.5,57 )g(t)=t38​,(1.5,57)

Find the Slope of the Tangent Line to the Graph $g ( t ) = \frac { 8 } { t ^ { 3 } } , ( 1.5,57 )$