Đáp án: 

$\textbf{a}\bigg)$ Sai

$\textbf{b}\bigg)$ Đúng

$\textbf{c}\bigg)$ Sai

$\textbf{d}\bigg)$ Sai

Giải thích các bước giải:

$\textbf{a$\bigg)$} x(t) = t^3 - 6t^2 + 9t$

$\Rightarrow v(t) = x'(t) = (t^3)' - 6(t^2)' + 9t'$

$= 3t^2 - 6(2t) + 9$

$= 3t^2 - 12t + 9$

$\Rightarrow$ Sai

$\textbf{b$\bigg)$} v(t) = 3t^2 -12t + 9$

$\Rightarrow a(t) = v'(t) = 3(t^2)' - 12t' + 9'$

$= 3(2t) - 12 + 0$

$= 6t - 12$

$\Rightarrow$ Đúng

$\textbf{c$\bigg)$} v'(t) = 0 \Leftrightarrow 6t - 12 = 0$

$\Leftrightarrow t = 2$

$v'(t) > 0$ khi $t \in (2; + \infty)$

$\Rightarrow v(t)$ tăng khi $t \in (2; +\infty)$

$\Rightarrow$ Sai

$\textbf{d$\bigg)$} v'(t) < 0$ khi $t \in (-\infty; 2)$

$\Rightarrow v(t)$ giảm khi $t \in (-\infty; 2)$

$\Rightarrow$ Sai