Function

[ x(t) = a + bt, y(t) = c + dt, z(t) = e + ft ]

Domain

t is an element of the set of all Real numbers

Graphs

Derivative

With respect to t: [b, d, f]

Since for each section, the value is a constant, and since the constants in the graph are non-zero, they will never equal 0 and there are no critical points. This means that there are no minimums or maximums. This is shown in the graph by the fact that the spring will expand up and down to infinity.

Integral

With respect to t: [a*t + ( ¹/₂ )b*t², c*t + ( ¹/₂ )d*t², e*t + ( ¹/₂ )f*t²]

Interesting Features

When working with this function, there are many different items to look at. The a, c, and e are the coordinates of a point on the line. In the graph, the point is (0, 0, 0). The b, d, and f are the "slope" of each direction. In the graph, it goes up 1 unit in the x direction, 2 units in the y direction, and 3 units in the z direction.