The Surface of a Mountain Is Modeled by the Equation $h ( x , y ) = 4000 - 0.005 x ^ { 2 } - 0.007 y ^ { 2 }$

The surface of a mountain is modeled by the equation $h ( x , y ) = 4000 - 0.005 x ^ { 2 } - 0.007 y ^ { 2 }$ . A mountain climber is at the point $( 400,600,4390 )$ . In what direction should the climber move in order to ascend at the greatest rate? Round all numerical values in your answer to one decimal place.

A) $13.2 \hat { \mathbf { i } } - 8.4 \hat { \mathbf { j } }$
B) $- 6.4 \hat { \mathbf { i } } - 13.2 \hat { \mathbf { j } }$
C) $- 4.0 \hat { \mathbf { i } } - 8.4 \hat { \mathbf { j } }$
D) $10.8 \hat { \mathbf { i } } + 4.0 \hat { \mathbf { j } }$
E) $- 5.6 \hat { \mathbf { i } } + 10.8 \hat { \mathbf { j } }$