42. What is the greatest value of b for which any real valued function f that satisfies the following properties must also satisfy f(1)<5 ?

1> f is infinitely differentiable on the real numbers

2> f(0)=1, f'(0)=1, and f''(0)=2; and

3> |f'''(x)|< b for all x in [0,1]

a)1

b)2

c)6

d)12

e)24

23.Let f be a real valued function continuous on the close interval [0,1] and differentiable on the open interval (0,1) with f(0)=1 and f(1)=0. Which of the following must be true

1. there exists x in (0,1) such that f(x)=x

2. there exists x in (0,1) such that f'(x)=-1

3. f(x)>0 for all x in [0,1)

a) 1 only

b) 2 only

c) 1 and 2 only

d) 2 and 3 only

e) 1.2 and 3

Please post as soon as possible. I am in a big mess regarding this questions. Please Help.