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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 som…

Q1

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

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

d

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

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