Mathematical formulas that can be abandoned by the mean value theorem must be learned. If not, it is difficult for us to give a hint. First of all, you should remember those basic concepts and formulas. Learning mathematics mainly depends on the accumulation of problem-solving methods. Different types of problems have different methods to solve them. As long as you sum up the problem-solving methods, I believe your math scores will be greatly improved.
If you only ask for postgraduate mathematics, you can give up the proof question; If you want to get high marks, it is enough to do the first question of the proof.
Just like integral proof, two methods are easy to master: the first is to set the upper limit (lower limit) as a variable, and then analyze the property of the variable-limit integral function to verify it; The second is to use the mean value theorem flexibly. As for the partial second mean value theorem of integrals, and all kinds of complicated Taylor proofs in the exercise notes, you can put them directly.
Now I can't do anything about the mean value theorem, and I really don't want to throw it away. I didn't officially start studying advanced mathematics until the summer vacation. I passed the foundation and made the foundation of 1800. At present, the second round of mathematics has reviewed the derivative application part of the chapter of differential calculus, and the proof of mean value theorem and inequality is really not good, and it can not be written intuitively in the examination room.