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Optimization Problems Calculator

Closed-interval optimization calculator. Enter f(x) on [a,b] to scan the global max/min and their locations—for extrema applications.

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Compare critical points and endpoints → global maximum/minimum
Supports + - * / ^ and sin cos tan sqrt exp log pi e
Closed endpoint
Closed endpoint

📖 Tutorial｜Optimization Problems

1. Definition
A continuous function on a closed interval attains its max and min, either at stationary points (f′=0) or endpoints.
2. Symbols
SymbolMeaning
[a,b]Closed interval
f′=0Stationary candidates
Endpointsa and b
3. How it works
  • We densely sample f on the interval;
  • Find the smallest and largest values;
  • Approximate the global optima.
4. Steps
  1. Enter the objective f(x);
  2. Enter the closed interval [a,b];
  3. Click Calculate.
5. Example
Example: f=x² on [−2,3]. Min at x=0 is 0; max at endpoint x=3 is 9.
6. Pitfalls
Optima may be at endpoints, not only stationary points;
The scan is approximate;
Applied problems need an objective and a domain first.

❓ FAQ｜Optimization Problems

General steps for optimization?
Build the objective, fix the domain, find stationary points, compare with endpoints, answer the question.
Does a closed-interval extremum always exist?
Yes, by the extreme value theorem for continuous functions.
Max/min vs extrema?
Extrema are local; max/min are global and occur at extrema or endpoints.
Why is the result approximate?
We scan a grid; accuracy depends on density. Solve precisely when needed.
Does an open interval always have extrema?
Not necessarily; it may lack a max or min.