This topic examines the geometric meaning of derivatives, uses the basic knowledge and skills such as monotonicity extreme value and maximum value of derivatives to study functions, and examines the thinking method of classified discussion. The answer is here/exercise/math /8040 19. It is a difficult problem to examine reasoning ability and computing ability.

Let f (x) = alnx+(1-a) x2/2-bx (a is not equal to 1), and the tangent slope of curve y=f(x) at point (1,f( 1)) is 0.

(1) find b;

(2) If x0 exists, f (x0)

The topic doesn't look too difficult, but the thinking is rather chaotic.