Find the gradient field of the potential function below.

Question

Find the gradient field of the potential function below.

 

 

 

φ(x,y)=x^3+y+100

Answer 1

Grad(φ) = ∇f = (∂f/∂x, ∂f/∂y)

 

∇f = (3x², 1)

 

The vector field would be defined as increasing in the x-direction as x gets larger and increases in the y-direction by 1 at all points.