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Variation Table & Curve Analysis Online

Generate and edit a Variation Table, First Derivative Sign Chart or First and Second Derivative Analysis Table with exact critical values, concavity and inflection points.

Online Function Variation Table Functions · Parametric · Polar · Relations · Analysis
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Detailed instructions

Use this workspace from input to export

A dedicated page opens the correct tab. Save and Open preserve the editable Functions, Table, Shading, Revolution and Axes scopes together with their objects and images.

Quick guide

  1. Choose the function, then analyze its full domain or enter a custom From x / To x interval.
  2. Select Variation Table, First Derivative Sign Chart, or First and Second Derivative Analysis Table.
  3. Calculate and review the domain, limits, derivatives, roots, extrema, behavior, concavity and inflection information provided by the selected table type.
  4. Customize the frame and lines, edit or add objects, then Save or export PNG, SVG or Copy.

Three table types

  • Variation Table: x, f′(x) and f(x) rows with derivative signs, arrows, extrema, infinities and discontinuity markers.
  • First Derivative Sign Chart: intervals, sign of f′(x), function behavior and f(x).
  • First and Second Derivative Analysis Table: signs of f′(x) and f″(x), increasing/decreasing behavior, concavity and inflection points.
  • English pages default to the First Derivative Sign Chart; Vietnamese, French, Simplified Chinese, Spanish, German, Japanese, Brazilian Portuguese, Korean, Italian, Indonesian, Hindi, Thai and Arabic pages default to the Variation Table. The Table type selector can change any page.

Exact analysis and review

  • The tool analyzes the real domain, boundary limits, derivative and sign intervals, with CAS verification when available.
  • Fractions, roots, π and e are preserved in exact values whenever the calculation can determine them.
  • Critical points, zeros, extrema or stationary points are placed at the appropriate table columns.
  • The First and Second Derivative Analysis Table adds second-derivative signs, concavity and inflection-point information; review the generated result before using it in a final document.

Edit and format the table

  • Choose no outer rectangular frame or a full frame, and set horizontal/vertical line color, thickness and solid/dashed/dotted style.
  • Format all arrows, row labels, numbers, infinities and plus/minus signs as groups.
  • Double-click text, formulas, arrows or markers to edit them individually; drag, rotate or delete selected objects.
  • Insert new text, Alpha formulas, images, lines or arrows. Images support resize, rotation and Front/Back layers.

Edit, save and export

  • Use A to insert editable plain text or an Alpha Formula. Insert images from the device, and add Line or Arrow objects where those buttons are available.
  • Select and drag objects directly. Double-click an object to edit it; image handles resize or rotate it, and Front/Back controls set its layer.
  • Undo and Redo include drawing changes, object edits, table edits, inserted images and axis customizations.
  • Save downloads a portable .ogp project containing Functions, Table, Shading, Revolution, Axes and their editable objects. HTML creates a launcher that restores the same saved scopes in a real OnlineGraphing.com tab.
  • Open loads a saved .ogp project. PNG and Copy create raster output, while SVG remains vector-based and stays sharp when enlarged.

Changing a table object does not change the original function formula. Recalculate when you want the table to be rebuilt from the mathematical analysis.

Tip: save an .ogp project before making major changes so supported editable content can be restored later. The project file does not include Analysis results or entries from the Points tab.

Need every control explained?
Open the complete user guide