ClearAll; hour[k_] = Table[24 k + i - 25,{i,25}];
tide2 = {4.2, 3.8, 3.3, 3.0, 2.8, 3.1,
          3.6, 4.5, 5.3, 6.0, 6.2, 5.8,
          5.1, 4.3, 3.4, 2.6, 2.0, 1.6,
          1.6, 2.2, 3.1, 3.9, 4.5, 4.7,
          4.6};
data = Map[Thread,Transpose[{hour[2],tide2}]];
lp:= ListPlot[data]; interp = Interpolation[data];
plot:= Plot[interp[t],{t,24,48},PlotPoints->100];
Show[lp,plot,AxesOrigin->{23,1.25},
	 AxesLabel->{"t","y"}, PlotLabel->"y = f(t)"]
FindMinimum[interp[t],{t,40}]
FindMinimum[-interp[t],{t,33}]