Let the Temperature in a Flat Plate Be Given by the Function

Essay

Let the temperature in a flat plate be given by the function $T ( x , y ) = 3 x ^ { 2 } + 2 x y$ . What is the value of the directional derivative of this function at the point $( 3 - 6 )$ in the direction $\mathbf { v } = 4 \mathbf { i } - 3 \mathbf { j }$ ? In what direction is the plate cooling most rapidly at $( 3 , - 6 )$ ?