Answer to Question #138614 in Differential Geometry | Topology for anjali g

Question

Sketch the gradient field ∇f of the following functions:
f(x , y) = (x^2 −y^2)/4

Answer 1

$\bigtriangledown (f) =<f_{x},f_{y}>=<\dfrac{x}{2},-\dfrac{y}{2}>$ Hence for sketching, the vector with initial point $(x,y)$points parallel to the vector $(\frac{x}{2},-\frac{y}{2}).$ So the gradient looks like