But if you only seek the extreme value of the topic, the question type is fixed and there are not many questions. It is a routine, a derivative list, and there is no thinking content. Do more and summarize more, and refer to the answers to sort out ideas.
If it is a big derivative problem of other comprehensive types, the last problem is another matter.
Basic steps to solve the extreme value problem of unary function;
1) to find the first derivative of the original function, so that the first derivative is equal to zero, and the stagnation point coordinates are obtained;
2) Find the second derivative of the original function and judge whether the stagnation point is an extreme point;
(2. 1) If the value of the second derivative at the stagnation point is greater than zero, take the minimum value;
(2.2) When the value of the second derivative at the stagnation point is less than zero, take the maximum value;
The necessary and sufficient conditions for the function y=f(x) to monotonically increase (monotonically decrease) in the interval a and b are: f' (x) >; = 0(f '(x)& lt； =0),
F '(x)=0, but only at a few points.
1. Generally, we often divide the interval (a, b) into several subintervals by the point (i.e. the stagnation point) k at which the derivative f'(x) is 0. On these subintervals, we can judge the monotonicity of the function by the following methods:
2. Inference (sufficiency) If the derivative of the function is positive (negative) in a certain interval, that is, the function monotonically increases (or monotonically decreases) in this interval, the derivative is positive and the curve rises; The derivative is zero, and the curve does not rise or fall; When the derivative is negative, the curve drops.
That is, if the derivative f '(x) at the stagnation point is 0, both sides will inevitably go from rising to falling or from falling to rising because of the continuous function, and the function value at the stagnation point will be the extreme value of this region.
The derivation of liberal arts is not difficult. Keep practicing, and after a round of review, almost all derivatives can be taken off.