## Function

[x(t) = t cos(t), y(t) = t sin(t), z(t) = t]

## Domain

tis an element of the set of allReal numbers

## Graphs

## Derivative

With respect tot: [cos(t) - t sin(t), sin(t) - t cos(t), 1]Critical points are formed where all the derivatives equal 0. These critical points may be minimums, maximums, or saddle points. Since the final value is 1, and 1 will never equal 0, there are no critical points.

## Integral

With respect tot: [cos(t) + t sin(t), sin(t) - t cos(t), (]^{1}/_{2})t^{2}

## Interesting Features

This is a modified helix curve. While the function looks very similar, the results are very different. This is caused by the first

tcoefficient. This scales the level outward as the function raises. The final graph shows how the function flips and mirrors the upward spiral downward.

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