Solution: Let the function y=f(x).

To find its monotonicity, we usually find its derivative, y'=f'(x).

When f' (x) > 0, f(x) increases monotonically;

When f' (x) < 0, f(x) decreases monotonously;

When f'(x)=0, f(x) takes the extreme value.

Minimum value: Let the domain of function y=f(x) be I, and if there is a real number m satisfying:

① For any real number x∈I, there is f (x) ≥ m;

② x0∈I exists. Let f (x0)=M, then we call the real number m the minimum value of the function y=f(x).

Maximum: Let the domain of the function y=f(x) be I, and if there is a real number m satisfying:

① For any real number x∈I, there is f (x) ≤ m;

② x0∈I exists. Let f (x0)=M, then we call the real number m the maximum value of the function y=f(x).

Extended data:

Not every periodic function has a minimum positive period.

Periodic functions have the following properties:

(1) If T(T≠0) is the period of f(x), then -T is also the period of f(x).

(2) If T(T≠0) is the period of f(x), then nT(n is an arbitrary non-zero integer) is also the period of f(x).

(3) If T 1 and T2 are both periods of f(x), they are also periods of f(x).

(4) If f(x) has a minimum positive period T*, then any positive period t of f(x) must be a positive integer multiple of T*.

(5)T* is the minimum positive period of f(x), and T 1 and T2 are two periods of f(x) respectively, then T 1/T2∈Q(Q is a rational number set).

(6) If T 1 and T2 are two periods of f(x) and T 1/T2 is an irrational number, then f(x) does not have a minimum positive period.

(7) The domain m of the periodic function f(x) must be a set with unbounded sides.

Of the two linear function expressions:

When k and b in the expressions of two linear functions are the same, the images of the two linear functions coincide;

When k is the same and b is different in the expressions of two linear functions, the images of the two linear functions are parallel;

When k and b in two linear function expressions are different, the images of two linear functions intersect;

When k is different and b is the same in two linear function expressions, the two linear function images intersect at the same point (0, b) on the y axis;

When k in two linear function expressions is negative reciprocal, two linear function images are perpendicular to each other.

References:

Baidu Encyclopedia-Function