Question #138614
Sketch the gradient field ∇f of the following functions:
f(x , y) = (x^2 −y^2)/4
1
Expert's answer
2020-10-15T17:16:22-0400

(f)=<fx,fy>=<x2,y2>\bigtriangledown (f) =<f_{x},f_{y}>=<\dfrac{x}{2},-\dfrac{y}{2}> Hence for sketching, the vector with initial point (x,y)(x,y)points parallel to the vector (x2,y2).(\frac{x}{2},-\frac{y}{2}). So the gradient looks like


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