## Thomas' Calculus 13th Edition

Since, $D_u f = \nabla f \cdot u$ $f_x= 2x-3y \\ f_y=-3x+8y$ $\nabla f =(2x-3y) \ i +(-3x+8y) \ j$ $\implies \nabla f (1,2)=-4i+13j$ and $|\nabla f (1,2)|=\sqrt {(-4)^2 +(13)^2}=\sqrt {16+169}=\sqrt {185}$ The maximum rate of change in function $f$ is less than $14$; this means that there will be no direction equal to $14$.