Tangent lines

cu[x_]:=x^3-x;cud[x_]:=cu'[x];ptsl[m_,p_,x_]:=m (x-p[[1]])+ p[[2]]//Simplify

Manipulate[
Show[
Plot[
{cu[x],
ptsl[cud[a],{a,cu[a]},x]
},
{x,-1.5,1.5},PlotRange->{{-1.5,1.5},{-2.2,2.2}},PlotStyle->{Blue,Red},ImageSize->Small,
AspectRatio->4.4/3
],
Graphics[
{Black,
PointSize[.02],
Point[{a,cu[a]}],
}
]
],
{{a,-1},-1.5,1.5},
SaveDefinitions->True
]