MathDB

For a function f(x)\equal{}(\ln x)^2\plus{}2\ln x, let

C

be the curve y\equal{}f(x). Denote

A(a,\ f(a)),\ B(b,\ f(b))\ (a<b)

the points of tangency of two tangents drawn from the origin

O

C

and the curve

C

. Answer the following questions. (1) Examine the increase and decrease, extremal value and inflection point , then draw the approximate garph of the curve

C

. (2) Find the values of

a,\ b

. (3) Find the volume by a rotation of the figure bounded by the part from the point

A

to the point

B

and line segments

OA,\ OB

around the

y

-axis.

Problem Statement