Suppose That Over a Certain Region of Space the Electrical $V$

question 71

Multiple Choice

Suppose that over a certain region of space the electrical potential $V$ is given by $V ( x , y , z ) = 8 x ^ { 2 } - 7 x y + 7 x y z$ .
Find the rate of change of the potential at $( - 1,1 , - 1 )$ in the direction of the vector $\mathbf { v } = 7 \mathbf { i } + 10 \mathbf { j } - 8 \mathbf { k }$ .

• A) \(- 15.099\)
• B) \(14.569856\)
• C) 44
• D) 20
• E) \(- 0.96\)

---

Definitions:

Optic Tracts

Nerve pathways traveling from the optic chiasma to the thalamus in the brain, important for the transmission of visual information.

Diencephalon

The diencephalon is a region of the brain that includes structures such as the thalamus and hypothalamus, involved in sensory and autonomic functions.

Hypothalamus

A region of the brain responsible for hormone production and regulation of vital bodily functions, including temperature, hunger, and thirst.

Thalamus

In vertebrates, the portion of the diencephalon that passes on selected sensory information to the cerebrum.