Find All Possible Functions with the Given Derivative $y ^ { \prime } = 3 t - \frac { 4 } { \sqrt { t } }$

question 150

Multiple Choice

Find all possible functions with the given derivative.
- $y ^ { \prime } = 3 t - \frac { 4 } { \sqrt { t } }$

• A) \(3 t ^ { 2 } - \frac { 4 } { \sqrt { t } } + C\)
• B) \(t ^ { 2 } - 4 \sqrt { t } + C\)
• C) \(3 t ^ { 2 } - 8 \sqrt { t } + C\)
• D) \(\frac { 3 } { 2 } t ^ { 2 } - 8 \sqrt { t } + C\)

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Definitions:

Conservation

The principle that certain physical characteristics (such as volume, mass, or number) remain unchanged, even when their appearance changes, as understood in cognitive development.

Object Permanence

Object permanence is the understanding that objects continue to exist even when they cannot be seen, heard, or otherwise sensed, a key cognitive development in infancy.

Principle

A fundamental truth, law, doctrine, or motivating force, upon which others are based or from which others are derived.

Principle of Conservation

A concept in cognitive development theory that an object's volume, mass, or quantity remains the same despite changes in its shape or form, usually understood by children during the concrete operational stage.