(1) This problem is a constant problem. For the problem of constant compilation, the maximum value is generally required. The title says:
F(x)≥0 holds, which means that the minimum value of f (x) in the function definition domain should be greater than or equal to 0. On the other hand, if the topic says that f(x)≤0, it means that the maximum value of the function should be less than or equal to 0, then the problem is transformed into the problem of finding the maximum value of the function. Because the functions in high school are all elementary functions, they must be differentiable in the definition domain, so as long as you are in the definition domain. Therefore, it is also the minimum value (if there are maximum and minimum values, or there are boundary values, it is necessary to compare the maximum and minimum values according to the meaning of the question). The minimum value is that when x=lna, f(x) is the minimum value, that is, f(lna)≥0, and a≤ 1 is solved, and the maximum value of a is 65438+.
(2) This problem is still a constant problem, so the maximum value is still required. By linking the slope problem with the derivative, write the expression of AB slope, substitute it into the expression of g(x), which is the formula in the answer (the formula in the answer is actually a deformation of Lagrange's mean value theorem, because senior high school doesn't learn this theorem), and deform the formula to get G (x2)-mx2 > G. If AB's slope is greater than m, this condition will be transformed into G (x2)-mx2 > G (. These two formulas are equivalent under given conditions, so you can solve G (x2)-mx2 > G (x 1)-mx65438.
Now it is time to deal with the formula g (x2)-mx2 > g (x1)-mx1. The * * of this formula is different from the expressions on the left and right sides, so when you encounter this problem of proving constancy, you can consider it from this aspect. The specific method is to make a function F(x)= the title is F(x)=g(x)-mx, but when encountering X 1≠X2, you can directly make X 1 > X2, or X 1 < X2, which will be converted into f (x/kloc-. At this point, if you make x2 > x 1, then F(X) is a monotone increasing function (for this question), then the answer is as shown in the answer. If you make x2,
To sum up, only when F(X) monotonically increases, can the range of m be determined, so follow this idea to solve, use a basic inequality, and then determine the range of m.
(3) When encountering this kind of problem, we should first look at whether the given problem can be deformed, because if the problem is difficult to figure out, we will not directly put forward the core of the problem, and we need to observe it ourselves and then find the core problem. In this problem, there is obviously a (2n)^n on the right side of the inequality, which is the same as the form on the left side, so you should first deform it and change the formula into (1/2n) n. √e/(e- 1). At this time, it depends on whether you can think of the conditions for using the first problem. If you do, it is equivalent to giving you a basis for scaling, otherwise it is difficult to prove the desired result of the topic by scaling directly. At this time, you can make X= (as shown in the answer) according to the method shown in the answer. In fact, you can take one with you, that is, the question of E X ≥ is usually linked with the last question of the topic. If you encounter it, go up and see if you can answer it with proven conditions. Can think of, basically can do it. The last inequality on the right side of this problem is the summation of geometric series. Just do the math yourself.
Give you a suggestion, sort out this kind of problems, summarize the problem-solving skills, such as finding the same characteristics, the same form, or similar questions, and then summarize them into appropriate ways of understanding and consolidate them.
Pure hand tour, remember to adopt it ~