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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 Calculus, with Antilog Calculator (inverse logarithm) and Average rate of change calculator 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?

Checking a derivative or an integral you worked out by hand, finding where a function turns, and getting a numeric answer when no closed form exists.

What is the most common mistake?

Integrating across a discontinuity as if it were not there. A numeric method will happily return a finite value for an integral that diverges — check the domain before trusting the number.

What else is filed next to it?

Antilog Calculator (inverse logarithm), Average rate of change calculator and Bernoulli ODE Solver 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?

Symbolic results are exact; numeric ones come from adaptive quadrature or a standard step method, and the tool reports which. Where both are available, compare them — a large gap means the problem is ill-conditioned.

Further reading

All guides →
ExplainerThe Expected Value Is a Number That Never HappensOutcomes of 10, 20 and −5 with probabilities 0.5, 0.3 and 0.2 give an expected value of 10. Shift the probabilities slightly and it becomes 10.5 — a result none of the three outcomes can produce.ExplainerAn Error Bar That Shrinks Is Not the Standard DeviationFor 10, 12, 15, 11, 13, 14 the standard deviation is 1.87 and the standard error is 0.76. They answer different questions, and only one of them gets smaller as you collect more data.ExplainerAn r of 0.85 That Proves NothingFive points give r = 0.853, which sounds strong. The threshold for significance at five points is 0.878, so this one falls short — and a perfect parabola scores exactly zero.ExplainerQuadruple the Sample to Halve the IntervalA mean of 100 with a standard deviation of 15 over 30 observations gives 100 ± 5.37 at 95 %. Going to 120 observations gives ± 2.68 — exactly half, because the sample size enters under a square root.ExplainerThe Same Three Temperatures Give Three Different Coefficients of VariationFor 2, 4, 4, 4, 5, 5, 7, 9 the coefficient of variation is 42.76 %. It is the right tool for comparing spread across different scales — and completely wrong for any scale whose zero was chosen by convention.ExplainerThree Dice Cluster, and One Die Does Not3d6 and 1d20 have almost the same average and nothing else in common. Against a target of 12 the three dice are better, against 18 they are five times worse — and the calculator gives the exact figures rather than a simulation.