Using the vector difference quotient exploration tool

Interface notes

This tool allows you to visually explore difference quotients of vector valued functions of a real variable as described in the vector derivative discussion notes by controlling a parameter value t₀ and an increment Δt which, respectively, determine the input of a (space) position function at which a difference quotient is formed, and the change from this "base point" over which the difference quotient will be taken. Notice that, regardless of the value of t₀ (and the choice of sign for Δt), forcing |Δt| to be small causes the direction of the difference quotient vector to approach tangency to the space curve.