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.
What are the problems with college entrance examination derivatives?
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.
Skills and ideas for solving derivative problems
① Determine the domain of the function f(x) (please remember the most easily overlooked);
(2) Find the solutions of the equation f'(x)= 0, and the discontinuous points between these solutions and f(x) divide the region into several intervals;
③ study the symbol of intercellular f ′ (x), where f ′ (x) > 0 and the interval is increasing, otherwise it is decreasing. The mainstream questions and methods of mathematical derivatives in college entrance examination (1) Find the value of a parameter in a function or the value of a given parameter to find the derivative or tangent.
Generally speaking, the mild derivative problem will set such a problem in the first problem: if f(x) takes the extreme value when x=k, try to find the value of the parameter in the given function; Or the tangent of f(x) at (a, f(a)) is perpendicular to a known straight line, and try to find the values of parameters in a given function and many other conditions.
Although there are many tricks, it is easy to solve them as long as you understand that their essence is to examine everyone's ability to find derivatives. This is generally used to distribute points, so you must be calm when encountering such problems. The method is:
First, find the derivative function of a given function, and then take the above-mentioned first case as an example by using the known conditions given in the title: let x=k and the derivative of f(x) be zero, find the value of the parameters contained in the function, and then check whether it is the extreme value of the function at this time.