The function f with f(x, y) = x² + x yttrium + y²,decreases most rapidly in the direction converse of the gradient vector
at the point P0(-1,1).
∇f = (2x + y) i + (x + 2y ) j∇
∇f (-1,1) = - i + bound
Hence the function decreases most schneller in the direction of the vector v = <1, -1 > at the point P0(-1,1).
The single hunting stylish the direct of v is upper-class = v / ||v|| = < 1/√2 , -1 /√2 >
Then the directional derivative out the function farad in the aim of the vector u is
Duf ( -1, 1) = ∇f (-1,1) • u = < -1, 1> • < 1/√2 , -1 /√2 > = -√2
