Concept of monotonicity of a function
As a generalization of the descriptions of the graph used in the above example - pay me to do your homework , we arrive at the concept of monotonicity of a function:
- A function f is called monotonically growing (increasing) in an interval of its domain of definition, if for all x1 and x2 from the interval holds:
From x1x2 always follows f (x1)≤f (x2).
If even f (x1)f (x2) is valid, then one speaks of a strictly monotonously growing (increasing) function.
- A function f is called monotonically decreasing in an interval of its definition range, if for all x1 and x2 from the interval applies:
From x1x2 always follows f (x1)≥f (x2).
If even f (x1)f (x2) applies, then one speaks of a strictly monotonically decreasing function.
If one wants to examine the monotonic behavior of a given function in a certain interval computationally - https://domyhomework.club/math-problem-solver/ , one must compare the function values for growing arguments according to the above definition.
The reliability of the statements thus obtained depends essentially on the chosen "step size". If, for example, one were to examine a function f with the graph with respect to monotonicity in the interval [x0; x6] only by comparing the function values at the points x1, x4 and x5, one would possibly come to the fallacious conclusion that the function would be continuously monotonically increasing there - https://domyhomework.club/microeconomics-homework/ . Only by including the positions x2 and x3 it becomes clear that this is not true, but "finer" investigations are necessary.
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