Identify Any Points at Which the Folium of Descartes $x = \frac { 8 t } { 1 + t ^ { 3 } } , y = \frac { 8 t ^ { 2 } } { 1 + t ^ { 3 } } \text { is not }$

question 49

Multiple Choice

Identify any points at which the Folium of Descartes $x = \frac { 8 t } { 1 + t ^ { 3 } } , y = \frac { 8 t ^ { 2 } } { 1 + t ^ { 3 } } \text { is not }$ smooth. Round your answer to two decimal places, if necessary.

• A) not smooth when \(t = - 1.00\)
• B) not smooth when \(t = 0\)
• C) not smooth when \(t = 2.67 , - 2.67\)
• D) smooth everywhere
• E) not smooth when \(t = 2.67\)

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Definitions:

Fibula

A long, thin bone on the lateral side of the lower leg, parallel and next to the tibia.

Femur

The longest and strongest bone in the human body, extending from the hip to the knee, playing a crucial role in supporting the body’s weight in both static and dynamic positions.

Metacarpals

The five long bones in the hand located between the wrist and the fingers.

Phalanges

Bones of the fingers and toes in humans and other vertebrates, making up the digits.