MediumPartial derivatives

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.3 Tangent Planes and Linear Approximations, #34 · Multivariable Calculus · Partial derivatives

Starting from … show that Newton’s method goes to … and find…

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 $(a, 0)$ show that Newton’s method goes to $(0, - 2 a^{3})$ and find the next point $(x_{2}, y_{2})$ . Which numbers $a$ lead to convergence? Which special number $a$ leads to a cycle, in which $(x_{2}, y_{2})$ is the same as the starting point $(a, 0)$ ?

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

~8 minWritten answer · check your work with Lemma

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.3 Tangent Planes and Linear Approximations, #34

Stuck? A gentle nudge

No hints for this one.

Something off?

Workspace

Your working

Check your full solution

Attach photos of your pages (up to 3) or one PDF — or check what you typed above. Lemma reads the work and verifies the reasoning, not just the answer.

Your first check today doesn't need an account.

Your photos and PDFs are read once and not stored — only the transcription is kept.