Let $f ( x , y ) = x ^ { 2 } e ^ { y }$

question 76

Essay

Let $f ( x , y ) = x ^ { 2 } e ^ { y }$ and $P ( - 2,0 )$ .(a) Find the rate of change in the direction of $\nabla f ( P )$ .(b) Calculate $D _ { u } f ( P )$ where $\mathbf { u }$ is a unit vector making an angle $\theta = 135 ^ { \circ }$ with $\nabla f ( P )$ .

---

Definitions:

Integration Of Information

The process of combining data from different sources to generate a comprehensive understanding or to make decisions.

Pituitary Gland

A small endocrine gland in the brain that produces key hormones which regulate growth, metabolism, and reproduction.

External Sexual Organs

Refers to the sex organs outside the body that are involved in sexual reproduction and sexual pleasure.

GABA

A neurotransmitter in the brain that inhibits nerve transmission, playing a key role in reducing neuronal excitability throughout the nervous system.