Method:
1, image observation method
As mentioned above, in the monotonous interval, the image of increasing function is rising, and the image of subtraction function is falling. Therefore, in a certain interval, the function corresponding to the function image that has been rising monotonously increases in this interval; The function corresponding to the function image that has been declining monotonously decreases in this interval.
2. Derivation method
The derivative is closely related to the monotonicity of the function. It is another method to study functions, which opens up many new ways for it. Especially for specific functions, using derivatives to solve the monotonicity of functions is clear, clear, quick and easy to master, and using derivatives to solve the monotonicity of functions requires mastering the basic derivative formula skillfully.
If the function y=f(x) is differentiable in the interval d, if x∈D, there is always f' (x) >; 0, the function y=f(x) monotonically increases in the interval d; On the other hand, if x∈D and f' (x) are less than 0, the function y=f(x) is said to decrease monotonically in the interval d.
Extended data
Methods and steps of judging monotonicity of function
General steps to prove monotonicity of function f(x) in a given interval d by definition:
① let x 1, x2∈D, x1< x2;
② difference △ y = f (x1)-f (x2);
③ Deformation (usually factorization and formula);
(4) Symbol (i.e. judging the sign of △y);
⑤ Draw a conclusion (that is, point out the monotonicity of the function f(x) in a given interval d).
That is: value? →? Work? →? Deformation? →? Set the number? →? Draw a conclusion.
Baidu Encyclopedia-Monotonicity