Search results
Results from the WOW.Com Content Network
The first-derivative test depends on the "increasing–decreasing test", which is itself ultimately a consequence of the mean value theorem. It is a direct consequence of the way the derivative is defined and its connection to decrease and increase of a function locally, combined with the previous section.
In calculus, a function defined on a subset of the real numbers with real values is called monotonic if it is either entirely non-decreasing, or entirely non-increasing. [2] That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease.
In the case of a completely monotonic function, the function and its derivatives must be alternately non-negative and non-positive in its domain of definition which would imply that function and its derivatives are alternately monotonically increasing and monotonically decreasing functions.
A differentiable function f is (strictly) concave on an interval if and only if its derivative function f ′ is (strictly) monotonically decreasing on that interval, that is, a concave function has a non-increasing (decreasing) slope. [3] [4] Points where concavity changes (between concave and convex) are inflection points. [5]
The theorem states that if you have an infinite matrix of non-negative real numbers , such that the rows are weakly increasing and each is bounded , where the bounds are summable < then, for each column, the non decreasing column sums , are bounded hence convergent, and the limit of the column sums is equal to the sum of the "limit column ...
Make web pages easy to read for you! With simple keyboard shortcuts, you can zoom in or out to make text larger or smaller. In an instant, these commands improve the readability of the content you're viewing.
Here’s what the letters represent: A is the amount of money in your account. P is your principal balance you invested. R is the annual interest rate expressed as a decimal. N is the number of ...
A chain in this partial order is a monotonically increasing subsequence, and an antichain is a monotonically decreasing subsequence. By Mirsky's theorem, either there is a chain of length r , or the sequence can be partitioned into at most r − 1 antichains; but in that case the largest of the antichains must form a decreasing subsequence with ...