Chapter 17.1, Problem 44E

Gradient fields on curves For the potential function φ and points A, B, C, and D on the level curve φ (x, y) = 0, complete the following steps.

a. Find the gradient field F =∇φ

b. Evaluate F at the points A, B, C, and D.

c. Plot the level curve φ(x, y) = 0 and the vectors F at the points A, B, C, and D.

44. $\phi (x,y)=\frac{1}{2}{x}^2-y;$ A(−2, 2), B(−1, 1/2), C(1, 1/2), and D(2, 2)