A function $f: \mathbb{R^2} \rightarrow \mathbb{R}$ is given by $$f(x,y)=6x^2y-x^3y-xy^3+2y^3+x^2-10xy+y^2-4x+4y+2$$ Given the circle $C=\{(x,y) | (x-2)^2+y^2=2\}$. Imagine a point moving around C counter clockwise. Determine for each position of this point the directional derivative of f in the point and the direction the point is moving in
How can this be approached?