[tex]\bf s(t)=-0.00077t^3+0.03351t^2+0.069t\\\\
-----------------------------\\\\
\cfrac{ds}{dt}=-\cfrac{231}{1000000}t^2+\cfrac{3351}{50000}t+\cfrac{69}{1000}
\\\\\\
0=-\cfrac{231}{1000000}t^2+\cfrac{3351}{50000}t+\cfrac{69}{1000}[/tex]
notice, is a quadratic with a negative leading term's coefficient, so, is opening downwards
so, the highest point of it, will be at the vertex, so that'd be when the derivative is the highest
[tex]\bf \textit{vertex of a parabola}\\ \quad \\
y = {{ a}}x^2{{ +b}}x{{ +c}}\qquad
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)[/tex]
so the ferry was going the fastest at [tex]\bf -\cfrac{{{ b}}}{2{{ a}}} \ minutes[/tex]
