Find all possible functions with the given derivative.
-$$y ^ { \prime } = 8 x ^ { 2 } - 3 x$$
A) $\frac { 8 } { 3 } x ^ { 3 } - \frac { 3 } { 2 } x ^ { 2 } + C$
B) $\frac { 8 } { 3 } x ^ { 3 } + C$
C) $- \frac { 8 } { 3 } x ^ { 3 } - \frac { 3 } { 2 } x ^ { 2 } + C$
D) $\frac { 8 } { 3 } x ^ { 2 } + \frac { 3 } { 2 } x + C$

Question

Quizplus · Accepted Answer

To find the antiderivative of $y' = 8x^2 - 3x$, integrate each term separately. The antiderivative of $8x^2$ is $\frac{8}{3}x^3$, and the antiderivative of $-3x$ is $-\frac{3}{2}x^2$. Adding a constant $C$ gives the general solution $\frac{8}{3}x^3 - \frac{3}{2}x^2 + C$.

Find All Possible Functions with the Given Derivative y′=8x2−3xy ^ { \prime } = 8 x ^ { 2 } - 3 xy′=8x2−3x

Find All Possible Functions with the Given Derivative $y ^ { \prime } = 8 x ^ { 2 } - 3 x$