The derivative test of college entrance examination is mainly about the synthesis of test functions, the application of inequality and derivative, and the difficulty is moderate.

What types of problems are there?

① Find the monotone interval of the function by derivative, or judge the monotonicity of the function;

(2) Using derivative to find the extreme value and maximum value of the function;

③ Applying derivatives to solve inequality problems.

Do you have any problem-solving skills?

The problem-solving skills of derivatives are relatively fixed, and the general idea is as follows

① Determine the domain of the function f(x) (please remember the most easily overlooked);

(2) Find the solutions of equation f ′ (x) = 0, and the discontinuous points of these solutions and f(x) divide the domain into several intervals;

③ Study the symbol of intercellular F ′ (X). When f ′ (x) > 0, the interval is an increasing interval, otherwise it is a decreasing interval.

From these two steps, there is a classified discussion. The maximum value of the function may appear at the extreme point or the end point. Polynomial derivation is generally combined with inequality to find the range of parameters, which will change according to the topic. Then, some skills of doing the problem are summarized in detail.

Skill cracking+instance disassembly

1. If the topic examines the concept of derivative, it mainly examines the definition of derivative at one point and its geometric significance, and pays attention to distinguishing the difference between derivative and △ y/△ x.

2. If the topic examines the tangent of the curve, it is divided into two situations:

(1) With regard to the tangent of the curve at a certain point, find the tangent of the curve y=f(x) at a certain point P(x, y), that is, find the derivative of the function y=f(x) at point p, that is, the slope of the tangent of the curve at that point.

(2) Regarding the common tangent of two curves, if a straight line is tangent to two curves at the same time, it is called the common tangent of two curves.