Find the Directions in Which the Directional Derivative Of $f ( x , y ) = x ^ { 2 } y + x ^ { 3 }$

question 173

Short Answer

Find the directions in which the directional derivative of $f ( x , y ) = x ^ { 2 } y + x ^ { 3 }$ at the point $( - 1,2 )$ has the value 1.

---

Definitions:

Marginal Utility

The extra pleasure or benefit derived from the consumption or utilization of an additional unit of a product or service.

Marginal Utility

The additional satisfaction or usefulness obtained from acquiring or consuming one more unit of a good or service.

Risk Averse

A characteristic of individuals who prefer to avoid risk, choosing certainty over uncertainty even if it results in a potentially lower return.

Marginal Utility Function

A mathematical representation that describes how the utility or satisfaction derived from consuming an additional unit of a good changes as more of the good is consumed.