Consider the polynomial $$f ( x ) = 1 + 2 x + 3 x ^ { 2 } + 4 x ^ { 3 }$$ Let s be the sum of all distinct real roots of $\mathrm { f } ( \mathrm { x } )$ and let $\mathrm { t } = | \mathrm { s } |$. The function $f ^ { \prime } ( x )$ is A) increasing in $\left( - t , - \frac { 1 } { 4 } \right)$ and decreasing in $\left( - \frac { 1 } { 4 } , t \right)$ B) decreasing in $\left( - t , - \frac { 1 } { 4 } \right)$ and increasing in $\left( - \frac { 1 } { 4 } , t \right)$ C) increasing in (-t, t) D) decreasing in (-t, t)
Consider the polynomial
$$f ( x ) = 1 + 2 x + 3 x ^ { 2 } + 4 x ^ { 3 }$$
Let s be the sum of all distinct real roots of $\mathrm { f } ( \mathrm { x } )$ and let $\mathrm { t } = | \mathrm { s } |$.
The function $f ^ { \prime } ( x )$ is\\
A) increasing in $\left( - t , - \frac { 1 } { 4 } \right)$ and decreasing in $\left( - \frac { 1 } { 4 } , t \right)$\\
B) decreasing in $\left( - t , - \frac { 1 } { 4 } \right)$ and increasing in $\left( - \frac { 1 } { 4 } , t \right)$\\
C) increasing in (-t, t)\\
D) decreasing in (-t, t)