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.