calculus inflection, increasing, decreasing

1.On what interval the function f(x)=x/(x^2+1) increasing?

(a)[-1,1](b)[-inf,1] (c) [-1,2] (d) [-inf, 2]

2. find the interval on which the function f(x)=x+cosx 0<=x<=2pi is increasing

(a)(pi/3,5pi/3)

(b)5pi/3,2pi)

(c) (pi/2, 3pi/2)

(d)(0,2pi,)

(e)none

3.

How many pointsof inflection does f(x) =x^3e^(-x) have?

(a)0

(b)1

(c)2

(d)3

(e) none

4. consider the function f(x)=x^2 in interval [0,1/2].According to mean value theorem thre must be a number c in (0,1/2) such that f '(c)is equal to particular value d. what is d?

(a) 3/2

(b)1

(c) 1/2

(d)2

(e) none