Let $f ( x ) = x \left| x ^ { 3 } \right|$

question 11

Essay

Let $f ( x ) = x \left| x ^ { 3 } \right|$ .
a. Sketch the graph of $f$ .
b. For what values of $x$ is $f$ differentiable?
c. Find a formula for $f ^ { \prime } ( x )$ .

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Definitions:

Infundibulum

A funnel-shaped structure, found in various organs, such as the brain (connecting the hypothalamus to the pituitary gland) or in the reproductive system (the ovarian tube).

Fimbriae

Series of thread-like projections surrounding the ostium of the fallopian tube, involved in capturing the ovum after ovulation.

Mesometrium

The portion of the broad ligament of the uterus that provides support and vascular connections to the uterus.

Uterine Horn

One of the two tubes in some female mammals, including rodents and pigs, that extend from the sides of the uterus, where fertilization often occurs.