How to draw Gradients

Question

How I can draw the gradients on the tangent to level curves. Shall you give me a hint? For example: $f(x,y) = x^3 - y$ and at points $(0,0)$ $∇f(0,0) = (0,-1)$ . Therefore, How to represent of the gradient whose corresponding constrains ($f(x,y) \leq 0$) are binding at the points given above $(0,0)$.

Answer 1

The gradient as 0 is actually $(0,-1)$. The tangent plane at 0 is going through the origin with slope -1 along the y axis and 0 along the x axis.