Section 14.6: Directional Derivatives & Gradient Vector

If \(g(x, y) = x^2 + y^2 - 4x\), find the gradient vector \(\nabla g(1, 2)\) and use it to find 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.