Ads
related to: calculus maxima minima word problems worksheet 2nd grade math free
Search results
Results From The WOW.Com Content Network
Maxima and minima x 2: Unique global minimum at x = 0. x 3: No global minima or maxima. Although the first derivative (3x 2) is 0 at x = 0, this is an inflection point. (2nd derivative is 0 at that point.) Unique global maximum at x = e. (See figure at right) x −x: Unique global maximum over the positive real numbers at x = 1/e.
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).
Maxima and minima; First derivative test; Second derivative test; Extreme value theorem; Differential equation; Differential operator; Newton's method; Taylor's theorem; L'Hôpital's rule; General Leibniz rule; Mean value theorem; Logarithmic derivative; Differential (calculus) Related rates; Regiomontanus' angle maximization problem; Rolle's ...
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.
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.
The calculus of variations may be said to begin with Newton's minimal resistance problem in 1687, followed by the brachistochrone curve problem raised by Johann Bernoulli (1696). [2] It immediately occupied the attention of Jacob Bernoulli and the Marquis de l'Hôpital , but Leonhard Euler first elaborated the subject, beginning in 1733.