Answer to Question #138959 in Differential Geometry | Topology for anjali g

Question

Sketch the gradient field ∇f of the following functions:
(a) f(x ,y) = x^2 + y^2.

Answer 1

a) $\nabla f (x,y)=(2x,2y)$ At (x,y) co-ordinate we draw the vector parallel to (2x,2y) e.g. at (1,3) we draw the vector (2,6). So coordinate of its end point is (1+2,3+6)=(3,9).

So the co-ordinate of the final point of the vector with initial point (x,y) is (x+2x,y+2y)=(3x,3y)