$\mathbf{b})$

$f\left(x\right)\to f^{\prime }\left(x_0\right)=0$ 

$v^{\prime }\left(t_0\right)=0$ oraz $v^{\prime \prime }\left(t_0\right)<0$

$a\left(t_0\right)=0$ oraz $a^{\prime }\left(t_0\right)<0$

 $16-3t_0=0$

$3t_0=16|:3$

$t_0=\frac{16}{3}\approx 5\to t_0=5\mathrm{s}$

$a^{\prime }\left(t_0\right)=-3<0$

$v\left(5\right)=-2+16\cdot 5-1,5\cdot {\left(5\right)}^2=$

$=-2+80-1,5\cdot 25=$

$=78-37,5=40,5$

 $v_{\max }=40,5\frac{\mathrm{m}}{\mathrm{s}}$

$a\left(5\right)=16-5\cdot 3=16-15=1$

$a=1\frac{\mathrm{m}}{{\mathrm{s}}^2}$