If f(x)=3 x4+4 x3-12 x2+12, then f ( x ) is

Question

If f(x)=3 x4+4 x3-12 x2+12, then f ( x ) is (A) increasing in (-∞,-2) and in (0,1) (B) increasing in (-2,0) and in (1, ∞) (C) decreasing in (-2,0) and in (0,1) (D) decreasing in (-∞,-2) and in (1, ∞)

Tardigrade Admin · Accepted Answer

∵ f(x)=3 x4+4 x3-12 x2+12 f(x)=12 x3+12 x2-24 x =12 x(x2+x-2) =12 x(x-1)(x+2) From above it is clear that f(x) is increasing in (-2,0) and in (1, ∞)

Q. If $f (x) = 3 x^{4} + 4 x^{3} - 12 x^{2} + 12$ , then $f (x)$ is

increasing in $(- \infty, - 2)$ and in $(0, 1)$

increasing in $(- 2, 0)$ and in $(1, \infty)$

decreasing in $(- 2, 0)$ and in $(0, 1)$

decreasing in $(- \infty, - 2)$ and in $(1, \infty)$

$∵ f (x) = 3 x^{4} + 4 x^{3} - 12 x^{2} + 12 f (x) = 12 x^{3} + 12 x^{2} - 24 x$
$= 12 x (x^{2} + x - 2)$
$= 12 x (x - 1) (x + 2)$
From above it is clear that $f (x)$ is increasing in $(- 2, 0)$ and in $(1, \infty)$

Q. If f(x)=3x4+4x3−12x2+12, then f(x) is

increasing in (−∞,−2) and in (0,1)

increasing in (−2,0) and in (1,∞)

decreasing in (−2,0) and in (0,1)

decreasing in (−∞,−2) and in (1,∞)