Chapter 13 - Section 13.5 - Directional Derivatives and Gradient Vectors - Exercises - Page 720: 34

No

We know that $D_u f = \nabla f \cdot u$ $T_x= 2y$ and $T_y=2x-z$and $T_z=-y$ $\nabla T(1,-1, 1) =-2i+j +k $ and $|\nabla T(1,-1, 1)|=\sqrt {(2)^2 +(1)^2+(1)^2}=\sqrt {6}$ or, $|\nabla T(1,-1, 1)|=\sqrt {6}= 2.44$ Thus the minimum rate of change is $-\sqrt{6}\gt -3$.