Application of function increase and decrease judgment

For example, if you take the derivative of the function y=x+ 1/x, you can get y' =1-kloc-0//x 2, and then judge the relationship between y' and 0.

You can get the function increasing interval (-&; ，- 1]，[ 1，+& amp； ), decreasing interval (-1, 0), (0,1);

2. Integral

Applied to the calculation of function graph area

For example, find the area enclosed by the function y=sinx and the x axis in the interval (0, pi).

Graphics with solution steps at the bottom?

3. Markov process

Applied to the probability calculation of some independent events.

For example, to solve the random movement of an ant on an octahedron (6 vertices and 8 faces), what is the probability that the ant will start from one vertex to four adjacent vertices? Same = 1/4? Find the probability of ants returning to the starting point after n steps.

First of all, we should understand that this process of ant crawling satisfies the "Markov process"

Markov process definition: in the known current state? What is its future evolution under (present) conditions? Doesn't depend on its past evolution? (? Past? )? .

Secondly, the six vertices of an octahedron are divided into three categories, which are the starting point of ant crawling, the point that can be reached by one step and the point that can not be reached by one step. The transfer matrix between these three types of points can be obtained as follows.

100? 0? 1? 0

p(0)=0 10，，p( 1)= 1/4 1/2 1/4？ . . . p(n)=(p( 1))^n？ (p(n) stands for n-step transfer matrix)

00 1? 0? 1? 0

The probability of returning to the starting point after the last n steps is the first term in p(n).