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

Question

If f(x)=3x4+4x3-12x2+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, text 0) and in (0, 1) (D) decreasing in (-∞ ,-2) and in (1, text ∞ )

Tardigrade Admin · Accepted Answer

∵ f(x)=3x4+4x3-12x2+12 f(x)=12x3+12x2-24x =12x(x2+x-2) =12x(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 $(1, \infty)$

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

$∵$ $f (x) = 3 x^{4} + 4 x^{3} - 12 x^{2} + 12$ $f (x) = 12 x^{3} + 12 x^{2} - 24 x$
$= 12 x (x^{2} + x - 2)$
$= 12 x (x - 1) (x + 2)$
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,∞)

increasing in (−2,0) and in (0,1)

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