In problems 13, for each of the following functions
f defined on
[a, b] find the
c
on
[a, b] such that
f'(c) = 

Problem :
1) f (x) = x^{2}  4x on [2, 4]
f'(c)  =  = 2 

2c  4  =  2 

c  =  3 

Problem :
3) f (x) = on [1, 2]
Problem :
4) On the interval [5,5], there is no point at which the derivative of f (x) =x is
equal to zero, even though f ( 5) = f (5). Is this a contradiction of Rolle's theorem?
No, it isn't a contradiction, since this function is not differentiable on the entire interval
( 5, 5).
Problem :
Find the number c that satisfies Rolle's theorem for f (x) = sin(x) on the interval
[0, Π].
(sin(x))' = cos(x)
cos(x) = 0 at
x =