Question

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

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

Answer 1

Answer: (D)

$\left(-\infty, \frac{9}{2}\right)$

Answer 2

The correct answer is (D) : $\left(-\infty, \frac{9}{2}\right)$
f(x)=2x3+(2p−7)x2+3(2p−9)x−6
f′(x)=6x2+2(2p−7)x+3(2p−9)
f′(0)<0
∴3(2p−9)<0
p<29​
p∈(−∞,29​)