Sketch the Graph Of $y = x ^ { \frac { 1 } { 3 } }$

question 248

Essay

Sketch the graph of $y = x ^ { \frac { 1 } { 3 } }$ . Clearly the only x-intercept is zero. However, Newton's method fails to converge here. Explain this failure.

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Definitions:

Pollination

The transfer of pollen from the male anthers of a flower to the female stigma, essential for the fertilization and reproductive success of many plant species.

Stigma

In flowering plants, portion of the carpel where pollen grains adhere and germinate before fertilization can occur.

Pollen Grains

Microscopic structures containing male gametes that are transferred from the male anther to the female reproductive structure in plants.

Ovules

The structure within the ovary of seed plants that develops into a seed after fertilization.