A particle moves along a line by $s = t^{3} - 9 t^{2} + 24 t$ , then S is decreasing when t $ϵ$

(2, 4)

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Solution

The correct option is A $(2, 4)$
$S = t^{3} - 9 t^{2} + 24 t$
$S = 3 t^{2} - 18 t + 24 = 0$
$3 (t^{2} - 6 t + 8) = 0$
$t^{2} - 4 t - 2 t + 8 = 0$
$t (t - 4) - 2 (t - 4) = 0$
$(t - 4) (t - 2) = 0$
Decrease when $t \in [2, 4]$

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A particle moves along a line by s=t3−9t2+24t, then S is decreasing when t ϵ

The correct option is A (2,4)S=t3−9t2+24tS=3t2−18t+24=03(t2−6t+8)=0t2−4t−2t+8=0t(t−4)−2(t−4)=0(t−4)(t−2)=0Decrease when t∈[2,4]

A particle moves along a line by $s = t^{3} - 9 t^{2} + 24 t$ , then S is decreasing when t $ϵ$

The correct option is A $(2, 4)$
$S = t^{3} - 9 t^{2} + 24 t$
$S = 3 t^{2} - 18 t + 24 = 0$
$3 (t^{2} - 6 t + 8) = 0$
$t^{2} - 4 t - 2 t + 8 = 0$
$t (t - 4) - 2 (t - 4) = 0$
$(t - 4) (t - 2) = 0$
Decrease when $t \in [2, 4]$