r0={-1,1,-1};p=Point[{r0}];
ptest=ParametricPlot3D[{t,t^2,t^3},{t,-1.3,2
}
,AxesLabel->{x,y,z},Axes->True,PlotStyle->Directive[Blue,Thickness[0.02]]]

Manipulate[


Graphics3D[{
{Green, PointSize[0.08],Point[{{-1,1,-1},{(-1+h),(-1+h)^2,(-1+h)^3}}]},

{Red,
Thickness[0.015],
Arrow[{{-1,1,-1},r0+
(1/h)*({(-1+h),(-1+h)^2,(-1+h)^3}-r0)}
]},

{Purple,Thickness[0.001],
Arrow[{{-1,1,-1},
{(-1+h),(-1+h)^2,(-1+h)^3}}
]},

ptest[[1]]
}],


{h,3,0.03}
]

In purple: (OverVector[r])(t+h)-(Subscript[(OverVector[r]), 0]), as h runs from 3 to 0.03.
In red: ((OverVector[r])(t+h)-(Subscript[(OverVector[r]), 0]))/h