It does not mean that all derivatives with parameters should be classified when judging the monotonicity of the original function. Classification discussion in mathematics has always been a means to solve problems rather than an end. Let's discuss this problem by judging the monotonicity of the original function with your parameter derivative. Only when the derivative is positive and negative within this parameter range, it is necessary to classify and discuss it.

For example: f(x)=alnx, f' (x) = a/x.

Solution: x is always greater than 0, and a can get all real numbers. A > This time, people noticed that when a >; 0，f '(x)& gt； 0, f(x) increases monotonically; When a<0, f' (x) < 0, f(x) decreases monotonously; When a=0, f'(x)=0 and f(x)=0 are constant functions that do not increase or decrease. The value of a affects the positive and negative of f'(x), and it is impossible to summarize the different increase and decrease of f(x) in different situations with one case. At this time, it is necessary to discuss it in categories.

But if f(x)=alnx, a >；; 1, then f' (x) > at this time; 0 in a >; The value range of 1 is constant, and f(x) has been monotonically increasing in the case of topic setting, so it is not necessary to explain the same results reflected in different situations.

When there are many different situations to solve the problem, the reason for classified discussion is simple, that is, one-sided result cannot replace the solution of the whole problem.