The value of x for which the polynomial 2x3-9x2+12x+4 is a decreasing function of x, is:

Question

The value of x for which the polynomial 2x3-9x2+12x+4 is a decreasing function of x, is: (A)  -1 < x < 1  (B)  0 < x < 2  (C)  x > 3  (D)  1 < x < 2

Tardigrade Admin · Accepted Answer

∵ f(x)=2x3-9x2+12x+4 On differentiating w.r.t. x, we get f(x)=6x2-18x+12 For function to be decreasing f(x)<0 ⇒ 6(x2-3x+2)<0 ⇒ (x2-2x-x+2)<0 ⇒ (x-2)(x-1)<0 ⇒ 1 < x < 2

Q. The value of $x$ for which the polynomial $2 x^{3} - 9 x^{2} + 12 x + 4$ is a decreasing function of $x,$ is:

$- 1 < x < 1$

$0 < x < 2$

$x > 3$

$1 < x < 2$

$1 < x < 3$

$∵$ $f (x) = 2 x^{3} - 9 x^{2} + 12 x + 4$
On differentiating w.r.t. $x,$ we get
$f (x) = 6 x^{2} - 18 x + 12$ For function to be decreasing $f (x) < 0$
$\Rightarrow$ $6 (x^{2} - 3 x + 2) < 0$
$\Rightarrow$ $(x^{2} - 2 x - x + 2) < 0$
$\Rightarrow$ $(x - 2) (x - 1) < 0$
$\Rightarrow$ $1 < x < 2$

Q. The value of x for which the polynomial 2x3−9x2+12x+4 is a decreasing function of x, is:

−1<x<1

0<x<2

x>3

1<x<2

1<x<3

∵ f(x)=2x3−9x2+12x+4 On differentiating w.r.t. x, we get f(x)=6x2−18x+12 For function to be decreasing f(x)<0 ⇒ 6(x2−3x+2)<0 ⇒ (x2−2x−x+2)<0 ⇒ (x−2)(x−1)<0 ⇒ 1<x<2