Calculus Calculators
Critical Point Calculator
Find where f′(x) = 0 and classify each as a maximum, minimum or inflection.
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What is Critical Points?
A critical point is where the derivative is zero, so the tangent is horizontal. The second derivative then classifies it: positive is a local minimum, negative a local maximum, and a sign change with f″ = 0 is an inflection point.
How it works
The derivative is computed symbolically, then scanned across the window for sign changes and each root is refined by bisection; the classification comes from the sign of f″ there. It is transparently numerical, so the page states the window it searched.
- Enter your input. Type or paste your input into the field above — the tool responds instantly.
- Review the result. Output updates live as you type. Everything runs entirely in your browser.
- Copy or download. Use the Copy button to grab the result, or Download to save it as a file.
Examples
Realistic sample
Type or paste any realistic input — the tool computes the result locally and instantly.
Common mistakes
Expecting a server round-trip
Nothing is uploaded — every tool in this category runs entirely in your browser.