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Mathematics for postgraduate entrance examination in 2006
This question is the first multiple-choice question in 2006, and even the position of the option has not changed.

[Solution 1]

Since it is a multiple-choice question, the better way is to draw pictures.

F'(x)>0 = & gtF(x) increases.

F''(x)>0 = & gtF(x) increases in a concave shape.

It can be seen from the figure that to choose a, of course, we must know the geometric meaning of dy and △ y.

The increment of dy tangent, and △y is the increment of function.

[Solution 2]

Properties of concave function;

F(x0+△x)>F(x0)+f'(x0)△x (△x is not equal to 0)

That is, f (x0+△ x)-f (x0) >: f' (x0) △ x >; 0(△x & gt; 0)

That is △ y > dy & gt0