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  "body": "\n## Summary\n\nLet $f$ be [[differentiable|0F1WR9C83K]] at $a$.\nThe tangent line to the graph of $f$ at $(a, f(a))$ is the line $y = f(a) + f'(a)(x - a)$.\nIt is the line through this point that best fits the graph near it.\n\n## Remarks\n\nThe tangent line is the limit of the secant lines through $(a, f(a))$ and $(x, f(x))$ as $x \\to a$.\nThe error $f(x) - f(a) - f'(a)(x - a)$ is $o(x - a)$ as $x \\to a$. This property characterizes the derivative.\nFor $f(x) = x^2$ at $a = 1$, the tangent line is $y = 2x - 1$.\n\n## Explanations\n\n### L1 human\n\nThe tangent line touches the graph at one point and has the same slope as the graph there.\nNear the point, the graph and the line are almost the same.\n",
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    "name": "Tangent line",
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    "sources": [
      {
        "locator": "Tangent line to a plane curve",
        "url": "https://en.wikipedia.org/wiki/Tangent"
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    "tag": "01R1HW3Y42",
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  "markdown": "https://math2.tamnd.com/node/01R1HW3Y42.md",
  "msc": [
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  "name": "Tangent line",
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  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/01R/01R1HW3Y42.md",
  "status": null,
  "tag": "01R1HW3Y42",
  "uri": "m2://01R1HW3Y42",
  "url": "https://math2.tamnd.com/wiki/tangent-line/",
  "writing": {
    "tag": "01R1HW3Y42",
    "kind": "concept",
    "level": "W1",
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