Let the function f(x)=2 x3+(2 p-7) x2+3(2 p-9) x-6 have a maxima for some value of x0. Then, the set of all values of p is

Question

Let the function f(x)=2 x3+(2 p-7) x2+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) ((9/2), ∞) (B) (0, (9/2)) (C) (-(9/2), (9/2)) (D) (-∞, (9/2))

Tardigrade Admin · Accepted Answer

f(x)=2 x3+(2 p-7) x2+3(2 p-9) x-6 f prime(x)=6 x2+2(2 p-7) x+3(2 p-9) f prime(0)<0 ∴ 3(2 p -9)<0 p <(9/2) p ∈(-∞, (9/2))

Q. 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

$(\frac{9}{2}, \infty)$

$(0, \frac{9}{2})$

$(- \frac{9}{2}, \frac{9}{2})$

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

$f (x) = 2 x^{3} + (2 p - 7) x^{2} + 3 (2 p - 9) x - 6$
$f^{'} (x) = 6 x^{2} + 2 (2 p - 7) x + 3 (2 p - 9)$
$f^{'} (0) < 0$
$∴ 3 (2 p - 9) < 0$
$p < \frac{9}{2}$
$p \in (- \infty, \frac{9}{2})$

Q. Let the function f(x)=2x3+(2p−7)x2+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

(29​,∞)

(0,29​)

(−29​,29​)

(−∞,29​)