Let $f ( x , y ) = \sqrt { 2 x + 3 y }$

question 222

Essay

Let $f ( x , y ) = \sqrt { 2 x + 3 y }$ .(a) In which direction does $f$ increase most rapidly at the point $( 3,1 )$ ?
(b) What is the maximum rate of change of $f$ at the point $( 3,1 )$ ?
(c) Find a unit vector $\mathbf { u }$ such that $D _ { u } f = 0$ at $( 3,1 )$ .

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Definitions:

Budget Line

An illustrative depiction of every possible pairing of two items that could be bought within a set budget at unchanging prices.

Slope

A measure of the steepness or incline of a line, often calculated as the ratio of the vertical change to the horizontal change between two points on the line.

Good A

A generic term often used in economics to describe a type of product or commodity.

Budget Line

A graphical representation of all possible combinations of two goods that a consumer can purchase with a given budget at prevailing prices.