Maximum & Minimum Value Calculator on an Interval
Maximum & minimum on a closed interval max f, min f on [a, b]
Enter f(x) and the endpoints a < b. The tool checks continuity, finds f'(x), solves f'(x) = 0, keeps the roots in (a, b), compares the values and states the maximum and minimum.
The calculator above finds the absolute maximum and minimum of a continuous function on a closed interval [a; b] by checking critical points and endpoints.
Formulas used
max = largest of f(a), f(b), f(xᵢ)
- xᵢ are the critical points in (a; b) where f′(x) = 0 or f′ does not exist.
- A continuous function on a closed interval always attains both a maximum and a minimum.
Worked example
f(x) = x³ − 3x on [0; 2]. Critical point x = 1:
max = 2 at x = 2, min = −2 at x = 1
Enter the same values in the calculator above to see every step of the solution.
How to use the calculator
- Type the function and the interval endpoints a and b.
- Press the calculate button. The result appears instantly.
- Read the step-by-step solution, rendered with KaTeX, to check your own work.