Homework Soursea Find the gradient of fx y sqrt2x2 2xy y2 b Evaluate the
(a) Find the gradient of f(x; y) = sqrt(2x^2 + 2xy + y^2)
(b) Evaluate the directional derivative of f(x; y) at the point P(1; 2) in
the direction from P(1; 2) to Q(2; 3).
(c) Find a unit vector in the direction of steepest decrease of f(x; y) at
the point P(1; 2). Also find the rate of decrease in this direction
(b) Evaluate the directional derivative of f(x; y) at the point P(1; 2) in
the direction from P(1; 2) to Q(2; 3).
(c) Find a unit vector in the direction of steepest decrease of f(x; y) at
the point P(1; 2). Also find the rate of decrease in this direction
Solution
a) grad(f) = (4x-2y)/2*sqrt(2x^2 + 2xy + y^2) i + (2y-2x)/2*sqrt(2x^2 + 2xy + y^2) j b) Directional derivative = Q-P = 1/sqrt(38) i
