Consider the level curves for F (x , y) = x² – y². y (a) How do we sketch in the gradient vectors? (b) Do we have a gradient vector at (0, 0)? -2 X (c) Where is the gradient vector longer: at (0.5,...

please explain mathematically

Extracted text: Consider the level curves for F (x , y) = x² – y². y (a) How do we sketch in the gradient vectors? (b) Do we have a gradient vector at (0, 0)? -2 X (c) Where is the gradient vector longer: at (0.5, 0.5) or at (1, 1)? Why? -1 -2 Hint: Gradient vectors are always normal to their associated level curves. They always point toward the next higher level curve. Gradient vectors are longer when the level curves are closer together (steepness). 2.