\(f(t)=-0,1t^3+3,4t^2-13,2t+234\)
\(f'(t)=-0,3t^2+6,8t-13,2\)
\(-0,3t^2+6,8t-13,2=0|:(-0,3)\)
\(t^2-\frac{68}{3}t=-44\)
\((t-\frac{34}{3})^2=-44+(\frac{34}{3})^2=-\frac{396}{9}+\frac{1156}{9}=\frac{760}{9}|±\sqrt{~~}\)
1.)
\(t-\frac{34}{3}=\frac{\sqrt{760}}{3}\)
\(t_1=\frac{34}{3}+\frac{\sqrt{760}}{3}≈20,5\)
2.)
\(t-\frac{34}{3}=-\frac{\sqrt{760}}{3}\)
\(t_2=\frac{34}{3}-\frac{\sqrt{760}}{3}≈2,14\)
Art der Extrema:
\(f''(t)=-0,6t+6,8\)
\(f''(20,5)=-0,6\cdot 20,5+6,8=-5,5<0\)Maximum
\(f''(2,14)=-0,6\cdot(2,14)+6,8>0\)Minimum
Um 2:08Uhr am Dienstag war der niedrigste Pegelstand.
Um 20:30Uhr am Dienstag war der niedrigste Pegelstand
