Find a Function Of $f ( x , y )$ Such That

question 143

Essay

Find a function of $f ( x , y )$ such that $\nabla f = \mathrm { F } ( x , y ) = \left\langle x y ^ { 2 } + 2 , x ^ { 2 } y + 2 \right\rangle$ .

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Definitions:

Cirque

A bowl-shaped, steep-walled mountain basin carved by glaciation, often serving as the birthplace of a glacier.

Moraine

Sediment carried by and deposited by a glacier; also refers to the resulting landform.

U-Shaped Valleys

Valleys characterized by steep sides and a rounded bottom, formed by the erosion of mountain glaciers.

Sharp Peaks

Pointed mountaintops or summit areas characterized by steep slopes and rugged terrain.