how can i know if the function is monoton or noSolutionThe t

how can i know if the function is monoton or no?

Solution

The term \'monotonic\' means \'no change\'.

A function y = g(x) is called monotonic on the interval I if it is either decreasing, increasing or constant.
1) A function g(x) is called decreasing if x1x1 > x2x2 and g(x1x1) < g(x2x2) for all x1x1, x2x2 in I.

2) A function g(x) is called increasing if x1x1 > x2x2 and g(x1x1) > g(x2x2) for all x1x1, x2x2 in I.

3)  A function g(x) is called constant if x1x1 > x2x2 and g(x1x1) = g(x2x2) for all x1x1, x2x2 in I.

We can determine if a function is monotonic by observing its graph, or we can check its derivative. A function is increasing when its derivative is positive, and it is decreasing when its derivative is negative.