Thinking about the third question, we want to look at the image, which can be easily obtained from (1) and (2): the maximum and minimum points of f(x) are: a (-k, -k/2/e), b (k, 0) respectively, and they increase monotonically on k, from -k to k. L, f(x) and y=m have three different intersections.

At this time, we know that f(x) and y=m must have an intersection on [-k, k], so we only need to consider when x>k and x < f(x) and y=m intersect on -k?

X> is at K. Since f(x) is continuous and f(x) is at K >, the minimum value at = 0 is equal to 0, so we only need to consider f(x) at K >. Maximum value on 0. F(x) in k >; 0 monotonically increases, if it is a real number for t, if there is x >；; K makes f(x)=t, then for any 0; 4k 2/e, which means that when m

So we can always get a positive integer n, which makes: n >；; 2k (just count down one by one on the number axis, because 2k and 2k+ 1 are finite numbers), let x=N, so:

f(x)=(N-k)^2 e^(N/k)

& gtk^2 e^2

& gt4k^2

& gt4k^2/e.

So we know that as long as 0

X<-K. A branch of 0 < f (x) < 4k^2/e。 Now only consider whether there is a t>0, so in X.

At this time, we encounter a problem: when X approaches negative infinity, (x-k) 2 approaches positive infinity, and E (x/k) approaches zero, what should their multiplication approach? Since f (x) = (x-k) 2e (x/k) = (x-k) 2/(e (-x/k)), let's consider g = | (x-k) 2 | = (x-k) 2, and h =| e.

To solve this problem, we can examine one thing: for any positive integer n, there is a positive integer x0; for any x>n, e x > x^n。 You can find n by mathematical induction.

So we get: x0>k>0, when X.

|f(x)|=|(x-k)^2 e^(x/k)|

=|(x-k)^2/x^3|*|x^3/e(-x/k)|

& lt|(x-k)^2/x^3|->； 0, when x approaches negative infinity.

So we know that when 0

To sum up, if f(x) and y=m must have three intersection rules: 0.

Idea: Find the maximum point, minimum point, lifting interval, draw a picture, compare, and then analyze and draw a conclusion.