Clear[f];f[x_]:=Sqrt[x]Sin[x]+1+x;a=1;
Manipulate[Show[Plot[{f[x],((f[a+Δx]-f[a])/(Δx))(x-a)+f[a]},{x,0,6},PlotRange->{{-0.1,6.5},{-0.1,5.5}},Ticks->None,PlotStyle->Thick,AxesStyle->Arrowheads[0.05],AxesLabel->{"x","f(x)"},LabelStyle->Directive[25]],Graphics[Text[Style["Δf(x)",20,Green],{0.6,(f[a]+f[a+Δx])/2}]],Graphics[Text[Style["Δx",20,Orange],{a+Δx/2,0.35}]],Graphics[{Green,Arrowheads[{-.025,.025}],Arrow[{{0.1,f[a]},{0.1,f[a+Δx]}}]}],Graphics[{Orange,Arrowheads[{-.025,.025}],Arrow[{{a,0.1},{a+Δx,0.1}}]}],Graphics[{Red,PointSize[0.02],Point[{a,f[a]}]}],Graphics[{Green,PointSize[0.015],Point[{a+Δx,f[a+Δx]}]}]],{Δx,5.5-a,0.00001,Appearance->{"Labeled"}},LabelStyle->Directive[25,Orange]]