MediumPartial derivatives

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.3 Tangent Planes and Linear Approximations, #33 · Multivariable Calculus · Partial derivatives

Starting from … find … which is also

This problem goes further with Newton’s method for $g = x^{3} - y$ and $h = y^{3} - x$ . This is Example 9 with solutions $(1, 1), (0, 0), (- 1, - 1)$ .

Starting from $(a, - a)$ find $Δ y$ which is also $- Δ x$ . Newton goes toward $(0, 0)$ . But can you find the sharp point in Figure 13.11 where the lemon meets the snake?

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, #33

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