First, the basic concept of vector

1, vector: A quantity with both magnitude and direction is called a vector. It is also called vector in physics. For example, force, velocity, acceleration and displacement are all vectors.

2. Parallel vectors: non-zero vectors with the same or opposite directions are called parallel vectors. Parallel vectors are also called * * * line vectors.

3. Equal vector: A vector with the same length and direction is called an equal vector.

Second, pay attention to the concept of vector.

1, vector is a quantity different from quantity, which has both magnitude and direction. No two vectors can be compared in size, only whether they are equal can be judged, but the modules of vectors can be compared in size.

2. Vector * * * lines are different from their directed line segments * * * lines. When the vector is a * * * straight line, the directed line segments representing the vector can be parallel, not necessarily on the same straight line; A directed line segment * * * means that the line segments must be on the same straight line.

3. According to the definition of vector equality, a vector can move in parallel at will as long as its size and direction remain unchanged. Therefore, when a vector is represented by a directed line segment, the starting point of the directed line segment can be arbitrarily selected, and any group of parallel vectors can be translated to the same straight line.

Third, find the monotonicity of the function:

The basic method of finding monotonicity of function by using derivative: Let function yf(x) be derivable in the interval (a, b), (1) If f(x) is constant, then function yf(x) is increasing function in the interval (a, b); (2) If F (x) is a constant, the function yf(x) is a decreasing function in the interval (a, b); (3) If f (x) is constant, the function yf(x) is a constant function in the interval (a, b).

Fourth, find the extreme value of the function:

Let the function yf(x) be defined in x0 and its vicinity. If all points near x0 have f(x)f(x0) (or f(x)f(x0)), it is said that f(x0) is the minimum (or maximum) of the function f(x).

Verb (abbreviation for verb) Find the value and minimum value of a function:

If the function f(x) has x0 in the domain I, so that there is always f(x)f(x0) for any xI, it is said that f(x0) is the value of the function in the domain. The extreme value of the function in the domain is not necessarily, but the maximum value in the domain is certain.