f(x)= x^( 3) +3x^( 2) −ax is decreasing on [ −1 , 2] then which is correct... 1: [ −3 ,24] 2: [ 24 , +∞) 3: (−∞ ,−3] 4 :(−∞, −3]∪[24, +∞)


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Question Number 184083 by mnjuly1970 last updated on 02/Jan/23

$f (x) = x^{3} + 3 x^{2} - a x i s$ $d e c r e a s i n g o n [- 1, 2]$ $t h e n w h i c h i s c o r r e c t . . .$ $1 : [- 3, 24]$ $2 : [24, + \infty)$ $3 : (- \infty, - 3]$ $4 : (- \infty, - 3] \cup [24, + \infty)$
	Answered by mr W last updated on 02/Jan/23

	$f (x) = x^{3} + 3 x^{2} - a x$ $f (- 1) = 2 + a$ $f (2) = 2 (10 - a) ⩽ 2 + a$ $\Rightarrow a ⩾ 6$ $f^{'} (x) = 3 {(x + 1)}^{2} - (3 + a)$ $f^{'} (- 1) = - (3 + a) ⩽ 0$ $\Rightarrow a ⩾ - 3$ $f^{'} (2) = 27 - (3 + a) ⩽ 0$ $\Rightarrow a ⩾ 24$ $s u m m a r y : a \in [24, + \infty) ✓$
	Commented by mnjuly1970 last updated on 04/Jan/23

	$p e a c e b e u p o n y o u s i r w$
	Commented by mr W last updated on 04/Jan/23

	$t h a n k s s i r!$
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