Find the critical number(s), if any of the function $f ( t ) = 3 t ^ { \frac { 3 } { 4 } } - 3 t ^ { \frac { 1 } { 4 } }$.
A) $\frac { 1 } { 3 }$
B) $\frac { 1 } { 9 }$
C) $0 , \frac { 1 } { 3 }$
D) $0 , \frac { 1 } { 9 }$

Question

Quizplus · Accepted Answer

Critical numbers are found by taking the derivative of the function and setting it equal to zero. The derivative of $f(t) = 3t^{3/4} - 3t^{1/4}$ is $f'(t) = \frac{9}{4}t^{-1/4} - \frac{3}{4}t^{-3/4}$. Setting $f'(t) = 0$ and solving for $t$ gives $t = 0$ and $t = \frac{1}{9}$, thus the critical numbers are $0$ and $\frac{1}{9}$.

Find the Critical Number(s), If Any of the Function f(t)=3t34−3t14f ( t ) = 3 t ^ { \frac { 3 } { 4 } } - 3 t ^ { \frac { 1 } { 4 } }f(t)=3t43​−3t41​

Find the Critical Number(s), If Any of the Function $f ( t ) = 3 t ^ { \frac { 3 } { 4 } } - 3 t ^ { \frac { 1 } { 4 } }$