The zero point of 1. function is often combined with derivative knowledge to judge the existence of unique zero point of function. When solving problems, it is often judged that a function has a zero point (existence) in a certain interval, and then the function monotonically increases (or monotonically decreases) (uniqueness) in the corresponding interval.

2. When the topic is not to find zero, but to find the range of parameters by using the number of zeros, the combination of numbers and shapes is generally adopted.

A template for solving inequality-related problems by derivative

To deal with binary inequality problems, it is often necessary to go through appropriate deformation treatment first, so as to flexibly construct functions and solve them by using the monotonicity of functions. The key points to solve such problems are as follows.

1. Appropriate deformation and flexible transformation. Combined with the conditions of the topic, it is sometimes necessary to "divide" the inequality with two variables, and then "replace" the local algebra with two variables, so as to equivalently transform the two-variable problem into a univariate problem; Sometimes it is necessary to transform the term so that both sides of the inequality have the same structural characteristics.

2. Construct the function and use the derivative. If it is transformed into a unary problem, you can directly construct a function and solve it with the derivative. If both sides of the transformed inequality have the same structural characteristics, a function can be constructed according to the structural characteristics and solved with the help of derivatives.