Find all possible functions with the given derivative.
-$$y ^ { \prime } = \frac { 3 } { 2 \sqrt { t } }$$
A) $\frac { 3 t ^ { 2 } } { 2 } + C$
B) $3 \sqrt { t } + C$
C) $\sqrt { t } + C$
D) $\frac { 3 t } { 2 } + C$

Question

Quizplus · Accepted Answer

To find the antiderivative of $y' = \frac{3}{2\sqrt{t}}$, we integrate the given function. The antiderivative of $\frac{1}{\sqrt{t}}$ is $2\sqrt{t}$, so the antiderivative of $\frac{3}{2\sqrt{t}}$ is $3\sqrt{t} + C$, where $C$ is the constant of integration.

Find All Possible Functions with the Given Derivative y′=32ty ^ { \prime } = \frac { 3 } { 2 \sqrt { t } }y′=2t​3​

Find All Possible Functions with the Given Derivative $y ^ { \prime } = \frac { 3 } { 2 \sqrt { t } }$