Chapter 13 - Section 13.5 - Directional Derivatives and Gradient Vectors - Exercises - Page 720: 33

No

$ f_x= 2x-3y$ and $ f_y=-3x+8y $ $\nabla f =(2x-3y) \ i +(-3x+8y) \ j $ and $\nabla f (1,2)=-4i+13j$ We know that $D_u f = \nabla f \cdot u$ Now, $|\nabla f (1,2)|=\sqrt {(-4)^2 +(13)^2}=\sqrt {185}$ We can see that the maximum rate of change in function $f$ is less than $14$, so we can conclude that there will be no direction equal to $14$.