ASSIGNMENT 7 SOLUTION - University of California, Berkeley

1. Stewart 14.6.48. [2 pts] If g(x; y) = x2 + y2 4x, nd the gradient vector rg(1; 2) and use it to nd the tangent line to the level curve g(x; y) = 1 at the point (1,2). Sketch the level curve, the tangent line, and the gradient vector. Solution: The gradient vector is. rg(1; 2) = hgx(1; 2); gy(1; 2)i = h 2; 4i. ................
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