Find the critical number(s), if any of the function $f(t)=2 t^{\frac{3}{4}}-4 t^{\frac{1}{4}}$
A) $\frac{4}{9}$
B) 0, $\frac{4}{9}$
C) $\frac{2}{3}$
D) 0, $\frac{2}{3}$

Question

Quizplus · Accepted Answer

To find the critical numbers, we first find the derivative of the function: $f'(t) = \frac{3}{2}t^{-\frac{1}{4}} - t^{-\frac{3}{4}}$. Setting $f'(t) = 0$, we solve $\frac{3}{2}t^{-\frac{1}{4}} = t^{-\frac{3}{4}}$, which simplifies to $t = \frac{4}{9}$. Additionally, $t = 0$ is a critical number because $f'(t)$ is undefined at $t = 0$.

Find the Critical Number(s), If Any of the Function f(t)=2t34−4t14f(t)=2 t^{\frac{3}{4}}-4 t^{\frac{1}{4}}f(t)=2t43​−4t41​

Find the Critical Number(s), If Any of the Function $f(t)=2 t^{\frac{3}{4}}-4 t^{\frac{1}{4}}$