If $f ( x , y ) = 2 x ^ { 2 } + 4 y ^ { 2 } - x y$

question 200

Essay

If $f ( x , y ) = 2 x ^ { 2 } + 4 y ^ { 2 } - x y$ , find the gradient at the point $( 2,1 )$ . Also find the rate of change of $f ( x , y )$ in the direction $\theta = \frac { \pi } { 3 }$ at $( 2,1 )$ .

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Definitions:

Standard Deviation

A statistical measure that quantifies the amount of variability or dispersion of a set of data points.

Capacity

The maximum amount of work that a system, facility, or workforce can produce or handle over a given period.

Expected Profit

The predicted amount of profit calculated by estimating revenues and subtracting estimated costs and expenses.

Landfill

A site for the disposal of waste materials by burying them, and is the oldest form of waste treatment.