Quote:

$\displaystyle \text{A particle moves on the }x\text{-axis so that its velocity at any time }t \ge 0$

$\displaystyle \text{is given by: }\: v(t)\:=\:12t^2-36t+15$

$\displaystyle \text{At }t = 1\text{, the particle is at the origin.}$

$\displaystyle \text{Find the maximum velocity of the particle for }0 \le t \le 2.$

$\displaystyle v' \:=\:24t-36 $

$\displaystyle 24t-36\:=\:0 \quad\Rightarrow\quad t \,=\,\frac{3}{2}$

$\displaystyle \text{I drew a sign chart, and I found that }\frac{3}{2}\text{ is actually the minimum.}$ . Right!

$\displaystyle \text{How can I get the maximum velocity?}$