MediumPartial derivatives

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.3 Tangent Planes and Linear Approximations, #30 · Multivariable Calculus · Partial derivatives

### RANGE 31-36 Problems 31–36 go further with Newton’s method for …

(a) To solve $g (x, y) = 0$ and $h (x, y) = 0$ is to find the meeting point of three surfaces: $z = g (x, y)$ and $z = h (x, y)$ and ______.
(b) Newton finds the meeting point of three planes: the tangent plane to the graph of $g$ , ______, and ______.

### RANGE 31-36
Problems 31–36 go further with Newton’s method for $g = x^{3} - y$ and $h = y^{3} - x$ . This is Example 9 with solutions $(1, 1), (0, 0), (- 1, - 1)$ .

This exercise builds on another exercise in its source book, which isn't shown here.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.3 Tangent Planes and Linear Approximations, #30

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