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  2. Fermat's theorem (stationary points) - Wikipedia

    en.wikipedia.org/wiki/Fermat's_theorem...

    Fermat's theorem is central to the calculus method of determining maxima and minima: in one dimension, one can find extrema by simply computing the stationary points (by computing the zeros of the derivative), the non-differentiable points, and the boundary points, and then investigating this set to determine the extrema.

  3. Maximum and minimum - Wikipedia

    en.wikipedia.org/wiki/Maximum_and_minimum

    Maximum and minimum. Local and global maxima and minima for cos (3π x )/ x, 0.1≤ x ≤1.1. In mathematical analysis, the maximum and minimum [a] of a function are, respectively, the largest and smallest value taken by the function. Known generically as extremum, [b] they may be defined either within a given range (the local or relative ...

  4. Derivative test - Wikipedia

    en.wikipedia.org/wiki/Derivative_test

    Derivative test. In calculus, a derivative test uses the derivatives of a function to locate the critical points of a function and determine whether each point is a local maximum, a local minimum, or a saddle point. Derivative tests can also give information about the concavity of a function. The usefulness of derivatives to find extrema is ...

  5. Stationary point - Wikipedia

    en.wikipedia.org/wiki/Stationary_point

    The stationary points are the red circles. In this graph, they are all relative maxima or relative minima. The blue squares are inflection points.. In mathematics, particularly in calculus, a stationary point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero.

  6. Critical point (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Critical_point_(mathematics)

    Critical point (mathematics) The (x-coordinates) of the red circles are ; the blue squares are . In mathematics, a critical point is the argument of a function where the function derivative is zero (or undefined, as specified below). The value of the function at a critical point is a critical value. [1]

  7. Glossary of calculus - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_calculus

    calculus. (From Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus) [8] is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. Cavalieri's principle.

  8. Differential calculus - Wikipedia

    en.wikipedia.org/wiki/Differential_calculus

    Calculus. In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. [1] It is one of the two traditional divisions of calculus, the other being integral calculus —the study of the area beneath a curve. [2]

  9. Calculus of variations - Wikipedia

    en.wikipedia.org/wiki/Calculus_of_Variations

    t. e. The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. [a] Functionals are often expressed as definite integrals involving functions ...

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