Find all possible functions with the given derivative.
-$y ^ { \prime } = 3 - \frac { 1 } { x ^ { 2 } }$
A) $3 x - \frac { 1 } { x } + C$
B) $3 + \frac { 1 } { x ^ { 2 } } + C$
C) $3 x + \frac { 1 } { x } + C$
D) $3 - \frac { 1 } { x } + C$

Question

Quizplus · Accepted Answer

To find the original function, we need to integrate the given derivative. We apply the power rule of integration which gives us:
$$y = \int \left(3 - \frac{1}{x^2}\right) dx = 3x + \frac{1}{x} + C$$
where C is the constant of integration. This matches Choice C, so it must be the correct answer.

Find All Possible Functions with the Given Derivative y′=3−1x2y ^ { \prime } = 3 - \frac { 1 } { x ^ { 2 } }y′=3−x21​

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