Differentiation

1) If c be a positive constant and | f(y) - f(x)| ≤ c(y-x)², then for all real x and y,then

a)f(x)=0 for all x
b)f(x)=x for all x
c)f '(x)=0 for all x
d)f '(x)=c for all x

2) If P(x) = x(x+1)(x+2)........(x+2004),then for positive real number x,

a)P(x)P''(x) > (P'(x))²
b)P(x)P''(x) < (P'(x))²
c)P(x)P''(x) = (P'(x))²
d) None of these.