Let the function $$f(x) = 2x^3 + (2p - 7)x^2 + 3(2p - 9)x - 6$$ have a maxima for some value of $$x 0$$. Then, the set of all values of $$p$$ is:

C. $$\left( -\infty, \dfrac{9}{2} \right)$$

A. $$\left( \dfrac{9}{2}, \infty \right)$$

B. $$\left( 0, \dfrac{9}{2} \right)$$

D. $$\left( -\dfrac{9}{2}, \dfrac{9}{2} \right)$$

Let the function f(x) = 2x³ + (2p - 7)x² + 3(2p - 9)x - 6 have a… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 25 January, Shift 2Applications of Derivatives (Monotonicity, Extrema)

Let the function $f(x) = 2x^3 + (2p - 7)x^2 + 3(2p - 9)x - 6$ 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:

A
$\left( \dfrac{9}{2}, \infty \right)$
B
$\left( 0, \dfrac{9}{2} \right)$
C
$\left( -\infty, \dfrac{9}{2} \right)$
D
$\left( -\dfrac{9}{2}, \dfrac{9}{2} \right)$

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