6. Background Story: The gradient of a level curve is orthogonal to the level curve containing it. In this question, explore the concepts. Questions: Consider g(x, y) = x² + y² - 5x. (A) (1.5 points) Find the gradient vector of g at P(3,2). (B) (0.5 points) Is (3,2) on the level curve g(x, y) = -2? Why? (C) (0.5 points) Use the Vg(3.2) to find the tangent line to the curve g(x, y) = -2 at (3,2). (D) (1 point) Sketch the level curve g(x, y) = -2 and the Vg(3.2) at point (3,2).

Fig: 1