$\text { Find the second derivative of the function } f ( x ) = \frac { 3 x ^ { 2 } + 5 x - 4 } { x } \text {. }$
A) $f ^ {tt } ( s ) = - \frac { 8 } { x ^ { 3 } }$
B) $f ^ { tt } ( s ) = \frac { 8 } { x ^ { 3 } }$
C) $f ^ {tt} ( s ) = - \frac { x + 8 } { x ^ { 3 } }$
D) $f ^ { tt } ( s ) = \frac { 4 } { x ^ { 3 } }$
E) $f ^ { tt } ( s ) = - \frac { 8 } { x ^ { 2 } }$

Question

$\text { Find the second derivative of the function } f ( x ) = \frac { 3 x ^ { 2 } + 5 x - 4 } { x } \text {. }$ 
A) $f ^ {tt } ( s ) = - \frac { 8 } { x ^ { 3 } }$
B) $f ^ { tt } ( s ) = \frac { 8 } { x ^ { 3 } }$
C) $f ^ {tt} ( s ) = - \frac { x + 8 } { x ^ { 3 } }$
D) $f ^ { tt } ( s ) = \frac { 4 } { x ^ { 3 } }$
E) $f ^ { tt } ( s ) = - \frac { 8 } { x ^ { 2 } }$

Quizplus · Accepted Answer

First, simplify $f(x) = 3x + 5 - \frac{4}{x}$. The first derivative $f'(x) = 3 + 0 + 4x^{-2}$, and the second derivative $f''(x) = 0 - 8x^{-3}$, which simplifies to $-\frac{8}{x^3}$.

Find the second derivative of the function f(x)=3x2+5x−4x. \text { Find the second derivative of the function } f ( x ) = \frac { 3 x ^ { 2 } + 5 x - 4 } { x } \text {. } Find the second derivative of the function f(x)=x3x2+5x−4​.

$\text { Find the second derivative of the function } f ( x ) = \frac { 3 x ^ { 2 } + 5 x - 4 } { x } \text {. }$