6 background story the gradient of a level curve is orthogonal to the
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).
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