[d-morrison]

Requested by Ezra · project thread

Adds a figure to exm-newton-maximum: the cubic f(x) = x³/3 − 4x, its downward-opening quadratic model at the start −2.5, the model's stationary point −2.05, and the local maximum at −2. R (ggplot2) and Python (matplotlib) tabs; cited from and nested in the example.

Part of #646 (figures for the optimization examples), under #579.

Files:

• _subfiles/vector-calc/_fig-newton-maximum.qmd (new)
• _subfiles/vector-calc/_exm-newton-maximum.qmd

Rendered optimization-newton.qmd locally and checked both figures.

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Claude finished review — View run

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Nothing blocking in this PR. I did not render the page, so the figure itself is unchecked.

I checked these:

• Plotted numbers: The Newton-step values are correct for f(x) = x³/3 − 4x. At x = −2.5, f′ = 2.25 and f″ = −5, so the model is f₀ + 2.25·dx − 2.5·dx². Its stationary point is at dx = 0.45, which is −2.05, matching the figure and the alt text. The local maximum at −2 gives f = 16/3, and the y-limits (−2, 6.5) contain every plotted point.
• Cross-references: #def-cubic-polynomial is defined in _subfiles/algebra/_def-quadratic-cubic.qmd. #def-newton-step, #def-stationary-point, #def-iterate and #def-local-maximizer are all defined under _subfiles/vector-calc/. The new figure is included only from _exm-newton-maximum.qmd, and that file is included once, from _sec_optimization_newton.qmd.
• Figure div: fig-newton-maximum is a figure div, not a theorem-type div, so the no-nesting rule doesn't apply. The R and Python tabs have matching alt text, colours and data. The variable prefixes and the \step macro follow the existing subfile conventions.

Suggestions (non-blocking)

• _subfiles/vector-calc/_fig-newton-maximum.qmd:106: the caption writes $f(x) = x^3 / 3 - 4x$ with a literal f. The example it points to already uses f and f'', so this matches the surrounding text. If latex-macros has a function-name macro for this f, use it there and in the example.
• _subfiles/vector-calc/_exm-newton-maximum.qmd:16: "the cubic" has an antecedent only if the reader remembers the earlier example. The caption does tie it to @exm-newton-maximum, so I'm leaving it as a suggestion.

Verdict

Ready for merge

Structured Review Data (JSON)

{
  "schema_version": "1.1",
  "reviewer": "claude",
  "commit_sha": "93c0694bd1ac25a2ff626a789500332e761736fe",
  "verdict": "CLEAN",
  "findings": [],
  "detailed_assessment": "Checked _fig-newton-maximum.qmd: the plotted quadratic model, stationary point at -2.05 and maximum at -2 are numerically correct, and all linked def ids resolve.",
  "holistic_assessment": "Small additive figure included once from the existing example; no regression, scope, or build-hygiene concerns, though the page was not rendered here."
}

I fetched PR #663 just now. It is open, not a draft and not merged. Its head is 93c0694bd1ac25a2ff626a789500332e761736fe, the commit I reviewed, so the verdict stands.

Verdict

Ready for merge

Structured Review Data (JSON)

{
  "schema_version": "1.1",
  "reviewer": "claude",
  "commit_sha": "93c0694bd1ac25a2ff626a789500332e761736fe",
  "verdict": "CLEAN",
  "findings": [],
  "detailed_assessment": "Checked _fig-newton-maximum.qmd: the plotted quadratic model, stationary point at -2.05 and maximum at -2 are numerically correct, and all linked def ids resolve.",
  "holistic_assessment": "Small additive figure included once from the existing example; no regression, scope, or build-hygiene concerns, though the page was not rendered here."
}

Reviewed commit: 93c0694

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💰 Cost: $0.2097 (review) — run

[github-actions]

PR Preview Action v1.8.2
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[d-morrison]

Annotations reviewed: 93c0694

All are platform notices (the ubuntu-latest migration, an empty SUBMODULES_TOKEN, a diff-highlight cap); none concern this change.

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Generated by Claude Code