Let f(x , y )= x^2+2xy+3y^2.   (a)  Compute the gradient of f(x,y) at the point (1,1). (b)  Compute the directional derivative of f(x,y) at the point (1,1) in the direction given by the vector <3,4>. (c)  Compute the directional derivative of f(x,y) at the point (1,1) in the direction given by the polar angle θ=3π/4 (d)  Compute the maximum value of the directional derivative of f(x,y) at the point (1,1).

Let f(x , y )= x^2+2xy+3y^2.

(a)  Compute the gradient of f(x,y) at the point (1,1).

(b)  Compute the directional derivative of f(x,y) at the point (1,1) in the direction given by the vector <3,4>.

(c)  Compute the directional derivative of f(x,y) at the point (1,1) in the direction given by the polar angle θ=3π/4

(d)  Compute the maximum value of the directional derivative of f(x,y) at the point (1,1).