1.

Image of f'(x):

The slope decreases gradually, but it is always f' (x) >: 0.

So it's obviously a convex function.

Image of 2, g'(x):

The slope increases gradually, but it is always f' (x) >: 0.

So it's obviously a concave function.

3. The functions f'(x) and g'(x) intersect, so f (x) and g (x) have points with equal slopes.

That is to say, if they intersect, they must be tangent; If they don't intersect, then the tangents at a certain point must be parallel.

Observe:

A, f(x) is a concave function and g(x) is a convex function.

B, f(x) is a convex function, and g(x) is a concave function without parallel tangents.

C, f(x) are concave functions, and g(x) are concave function errors.

D, f(x) are convex functions, and g(x) are convex functions with parallel tangents.