Question

Determine whether the Rolle's theorem can be applied to f on the closed interval (a,b) . I fi can be applied find all values of c, in the open interval such that fprime(c)=0

f(x)=3-|x-3|, [0,6]

Answer 1

f(x) is continuous on [0,6] and f(x) = 0 at both x=0 and x=6, so Rolle's Theorem applies. Therefore there is a value x=c such that f'(c) = 0

Answer 2

actually rolle's theorem does not apply because this function is not differentiable on [0,6]
there is not derivative at x = 3

Answer 3

i mean to say "there is no derivative at x = 3"