jee-main 2023 Q79

jee-main · India · session1_25jan_shift2 Stationary points and optimisation Determine parameters from given extremum conditions

Let the function $f ( x ) = 2 x ^ { 3 } + ( 2 p - 7 ) x ^ { 2 } + 3 ( 2 p - 9 ) x - 6$ have a maxima for some value of $x < 0$ and a minima for some value of $x > 0$. Then, the set of all values of $p$ is
(1) $\left( \frac { 9 } { 2 } , \infty \right)$
(2) $\left( 0 , \frac { 9 } { 2 } \right)$
(3) $\left( - \infty , \frac { 9 } { 2 } \right)$
(4) $\left( - \frac { 9 } { 2 } , \frac { 9 } { 2 } \right)$

Let the function $f ( x ) = 2 x ^ { 3 } + ( 2 p - 7 ) x ^ { 2 } + 3 ( 2 p - 9 ) x - 6$ have a maxima for some value of $x < 0$ and a minima for some value of $x > 0$. Then, the set of all values of $p$ is\\
(1) $\left( \frac { 9 } { 2 } , \infty \right)$\\
(2) $\left( 0 , \frac { 9 } { 2 } \right)$\\
(3) $\left( - \infty , \frac { 9 } { 2 } \right)$\\
(4) $\left( - \frac { 9 } { 2 } , \frac { 9 } { 2 } \right)$

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