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

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 $- 6 \mathbf { i } - \frac { 1 } { 4 } \mathbf { j }$ .