Extrema & Inflection Finder

Find maxima, minima, and inflection points of a function

About this calculator

The Extrema & Inflection Finder locates every local maximum, minimum, inflection point, and stationary saddle of f(x) on an interval. It scans 2000 samples for roots of f′ and sign changes of f″, then classifies each candidate with the first- and second-derivative tests, guarding against asymptote artifacts and floating-point noise so poles are never mistaken for extrema. Wholly undefined or constant functions are reported as such. Results list each point's coordinates, sorted by x, for calculus homework and curve sketching.

How to use the Extrema & Inflection Finder calculator

  1. Enter the values for your problem into the input fields.
  2. Read the result — it updates instantly as you type.
  3. Check the formula and the visual explanation to follow how the answer was found.
  4. Copy the page URL to share the exact calculation.

Common examples

  • x³ − 3x on [−3, 3] → maximum (−1, 2), inflection (0, 0), minimum (1, −2)
  • x³ on [−2, 2] → a saddle at (0, 0): horizontal tangent plus a concavity change
  • sin(x) on [0, 6.5] → maximum (1.570796327, 1), minimum (4.71238898, −1), inflections at 0, π, 2π
  • x⁴ − 2x² → minima at (−1, −1) and (1, −1), local maximum at (0, 0)

Frequently asked questions

How does the Extrema & Inflection Finder calculator work?

Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.

When would I use the Extrema & Inflection Finder calculator?

It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.

How accurate are the results?

Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.

Can I share a specific calculation with someone else?

Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.