The Surface of a Certain Lake Is Represented by a Region

Essay

The surface of a certain lake is represented by a region in the $x y$ -plane such that the depth under the point corresponding to $( x , y )$ is $f ( x , y ) = 300 - 2 x ^ { 2 } - 3 y ^ { 2 }$ . Zeke the dog is at the point $( 3,2 )$ .(a) In what direction should Zeke swim in order for the depth to decrease most rapidly?
(b) In what direction would the depth remain the same?