(1) When a=0, ① If the image of f(x) and the image of g(x) are tangent to the point P(x0, y0), find the values of x0 and b; ②f(x)=g(x) has a solution on [1, m], and find the range of b;

(2) When b=- 1, if f(x)≥g(x) is constant on [1/e, n], find the value range of a. 。

Test site: study the tangent equation of a point on the curve with derivative; Application of derivative in maximum and minimum problems.

Special topic: comprehensive application of derivatives.

Analysis: (1)① According to the fact that the tangent point is on the curve and the derivative at x=x0 is equal to the slope of the tangent, the values of x0 and b can be obtained by establishing the equation;

②f(x)=g(x) has a solution on [1, m], which can be transformed into y=b and h (x) = lnx/x.

There is an intersection point on [1, m], and then the range of h(x) on [1, m] is studied by derivation, so as to find the range of B;

(2) If f (x) ≥ g (x) holds on [1/e, n], A can be separated, and then the maximum value of the function on the other side of the inequality on [1/e, n] can be studied by derivative, so as to find out the value range of A. 。

Answer:

Comments: In this topic, the tangent equation at a certain point of the curve is investigated by derivative, and the monotonicity of function and the constancy of inequality are investigated by derivative. Generally, the problem of inequality constancy is solved by parameter separation method, maximum method and combination of numbers and shapes, which is an intermediate problem.

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