# Two more calculus problems

1. Nov 7, 2006

### oahsen

good days. i have two problems about calculus. could u help me ;
first is that;
consider the equation cot(pi*x)=x;
show t
hat this equation has exactly one solution rk in the Ik=(k,k+1) for every k<Z ( k<Z = k is a integer)

second is that ; show that for any differentiable function f(x) in the real line such that f(0)=0 , f(1)=1 , f(2)=4, there exist a point c in (0,2) such that f''(c)=2.

i think both of the problems are about the inter.value theo,mean value theo. and rolle theo. but i havent any idea of how can i solve.thanks for help...