Find All Possible Functions with the Given Derivative $$y ^ { \prime } = 3 - \frac { 1 } { x ^ { 2 } }$$

question 27

Multiple Choice

Find all possible functions with the given derivative.
- $$y ^ { \prime } = 3 - \frac { 1 } { x ^ { 2 } }$$

• A) \(3 + \frac { 1 } { x ^ { 2 } } + C\)
• B) \(3 - \frac { 1 } { x } + C\)
• C) \(3 x + \frac { 1 } { x } + C\)
• D) \(3 x - \frac { 1 } { x } + C\)

---

Definitions:

Experimental

Pertaining to a methodological approach that involves manipulating one variable to determine if changes in one variable cause changes in another variable.

Independent Variable

The variable in an experimental setup that is manipulated or changed to observe its effect on the dependent variable.

Dependent Variable

In an experiment, the variable that is being tested and measured; it is 'dependent' on the independent variable.

Control Variable

A factor that is kept constant to prevent its influence on the outcome of an experiment, ensuring that the experiment measures what it intends to.