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-

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 \dots

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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