Ask a number of points to prove the problem It is known that f (x) is differentiable on x > = A and f (a) = 0, b > 0, F'(x)+bF(x)>=0,x>=a When x > = a, f (x) > = 0,

Ask a number of points to prove the problem It is known that f (x) is differentiable on x > = A and f (a) = 0, b > 0, F'(x)+bF(x)>=0,x>=a When x > = a, f (x) > = 0,

Construct g (x) = e ^ (BX) f (x)
∴g(a)=0
∴g'(x)=e^(bx)(f'(x)+bf(x))≥0
x≥a ,g(x)≥g(a)=0
∴e^(bx)f(x)≥0
f(x)≥0

In senior high school mathematics proof questions, is the proof of less than or equal to a number the same as the proof of less than a number?
For example, is the proof of a ≤ 7 the same as that of a < 7? How to deal with such problems?

A = 7 means that being equal to or less than 7 is not and can be said, for example, 3 = 3
A "7" is sure to launch a "= 7 ah, with the idea of mathematical logic, you can do it yourself

Digital proof
It is known that in a tetrahedral ABCD, AC = BD, and E, F, G and H are the midpoint of edges AB, BC, CD and DA, respectively

Because e, F, G and H are the midpoint of edges AB, BC, CD and Da respectively
So EF / / AC GH / / AC AC = 2ef can get GH / / EF
Similarly, eh / / FG BD = 2eh can be obtained
So efgh is a parallelogram
And AC = 2ef, BD = 2eh and AC = BD
So the parallelogram efgh is a diamond