$\text { The temperature at the point } ( x , y ) \text { on a metal plate is modeled by }$

question 62

Multiple Choice

$\text { The temperature at the point } ( x , y ) \text { on a metal plate is modeled by }$ $T ( x , y ) = 200 e ^ { - \left( x ^ { 2 } + y \right) / 2 } , x \geq 0 , y \geq 0$ . Find the direction of greatest increase in heat from the point $( 4,15 )$ .

• A) The greatest increase is in the direction of the gradient \(- 4 \mathbf { i } - \frac { 1 } { 2 } \mathbf { j }\).
• B) The greatest increase is in the direction of the gradient \(- 4 \mathbf { i } - \frac { 1 } { 4 } \mathbf { j }\).
• C) The greatest increase is in the direction of the gradient \(- 6 \mathbf { i } - \frac { 1 } { 2 } \mathbf { j }\).
• D) The greatest increase is in the direction of the gradient \(- 8 \mathbf { i } - \frac { 1 } { 2 } \mathbf { j }\).
• E) The greatest increase is in the direction of the gradient \(- 6 \mathbf { i } - \frac { 1 } { 4 } \mathbf { j }\).

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