2. Substitution (trigonometric function, etc. Any alternative method you can think of to simplify the topic)

3. The maximum value of the derivative, derivative =0, and then look at the positive and negative derivatives on both sides (when calculating the maximum value, the size of the interval endpoint should be calculated at the same time).

4. Formula (the most basic method, the best method when no other method can be thought of)

5. Mean, Cauchy inequality (there are also some piano inequalities that may not be used, but they can be used to expand ideas and get answers in advance)

6. Combination of numbers and shapes (for example, finding the maximum value of a fraction (for example, the numerator is cosa+ 1 and the denominator is sina+ 1) can be regarded as the slope of the connecting line between (cosa, sina) and (-1,-1) in rectangular coordinate system); Another example is to convert the required formula into the distance between two points (especially what radical symbols appear); And the maximum value of the sum of absolute values. )

Generally speaking, derivation and inequality are tools; The replacement is to make better use of the above two tools; The combination of numbers and shapes is a good way to understand images. Generally, you should use it consciously when filling in the blanks. Even if you can't get the answer, it is very helpful to grasp the whole.

Note: Fractions generally need to be processed as follows to effectively separate variables: for example, x+1/x+2 =1-kloc-0//x+2.