Math problem for postgraduate entrance examination: Look at the following questions and choose D as the correct answer. Why are you more detailed? Say all the options.

According to the meaning of the question, when x1>; X2, f(x 1)>F(x2), that is, F(x) monotonically increases at (-∞,+∞).

If f(x) monotonically increases on (a, b), the derivative f' (x) of f(x) >: =0 holds on (a, b).

(1)

But (a) for any x, f' (x) >; 0, so it is wrong.

A counterexample: f (x) = x 3 is a simple increase, but when x=0, f'(x)=0.

(2)

According to the meaning of the question, when x1>; X2, both have f(x 1)>f(x2).

For any x, if f'(-x)≤0 and x∈(-∞, +∞), then -x∈(-∞, +∞).

Obviously, for any x, f'(-x)≤0 does not hold.

(3)

When x 1 >; At x2, if f(x 1)>F(x2), there is

When -x 1

(4)

According to the meaning of the question, when x1>; X2, both have f(x 1)>f(x2).

∴f(x) single increase

∴f'(x)≥0

∫-x 1 ≤- x2

∴f(-x 1)≤f(-x2)

That is, -f(x 1)≥-f(x2)

∴-f(-x) single increase

Obviously, you should choose D.

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