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Optimization calculator (calculus)

Find the minima and maxima of a function on an interval — the heart of every optimization problem. Enter f(x) and a range; it differentiates symbolically, locates the critical points where f′(x)=0, classifies each with the second derivative, and reports the global minimum and maximum on the interval.

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Optimization calculator (calculus) works straight from this page — free, instant, nothing to install. You will find it under Numbers & arithmetic, with Amicable Number Checker and Arctan2 Calculator (atan2 of y and x) for the neighbouring cases.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is Optimization calculator (calculus)?

Find the minima and maxima of a function on an interval — the heart of every optimization problem. Enter f(x) and a range; it differentiates symbolically, locates the critical points where f′(x)=0, classifies each with the second derivative, and reports the global minimum and maximum on the interval.

What does a concrete case look like?

f(x) = x³ − 3x, [−2, 2] → max 2 @ x = −1, min −2 @ x = 1 — the tool shows every step in between, not just the final figure.

When would I actually use this?

Reading a number written another way: a Roman numeral on a monument, a hexadecimal colour, a binary byte, or a fraction that needs reducing.

What is the most common mistake?

Assuming a decimal fraction survives a change of base. A tenth is exact in decimal and infinitely repeating in binary, which is why 0.1 + 0.2 is not 0.3 in most programming languages.

What else is filed next to it?

Amicable Number Checker, Arctan2 Calculator (atan2 of y and x) and Carry and borrow visualizer share its section. They are not variants of it — being filed together is not the same as being alike — but that is where to look if this turned out not to be the tool you wanted.

Where do the figures come from?

Base conversion and number-theory results are exact. Roman numerals follow the standard subtractive form used since the Middle Ages, which is not the only one the Romans themselves used.

Further reading

All guides →
How-toHow to Round Numbers: Round Half Up, Round Half to Even, and MoreRound to any decimal place or number of significant figures, and learn when to use round half up versus round half to even to avoid bias.ExplainerSignificant Figures Explained: Counting, Rounding, and Why They MatterLearn what counts as a significant figure, the rules for leading, trailing, and captive zeros, and how sig figs keep your calculated answers honest.How-toHow to Find Prime Factors: Factor Trees and the Division MethodBreak any whole number into its prime building blocks with a factor tree or repeated division — and write the result as a clean prime factorization with exponents.How-toHow to Multiply and Divide Fractions: Multiply Across, Flip to DivideMultiplying fractions needs no common denominator — just multiply across. Dividing means multiplying by the reciprocal. Learn both with worked examples and how to simplify.How-toHow to Add and Subtract Fractions: Common Denominator, Combine, SimplifyYou can only add or subtract fractions that share a denominator. Learn to find a common denominator, combine the numerators, and simplify the result, with a worked example.How-toHow to Do Long Division: Divide, Multiply, Subtract, Bring DownLong division breaks a big division into a repeating four-step cycle. Learn the divide-multiply-subtract-bring-down loop and how to read the remainder, with a worked example.