Question

Determine whether Rolle’s Theorem can be applied to f (x) 3-| x-3 | on the interval [0, 6]. If so, find all values of c in (0, 6) such that f’(c) = 0. If not, explain why not.

Answer 1

what are the conditions for roll's theorem?

Answer 2

The theorem states that if a real valued function f is :

1) continuous on a closed interval [a, b],
2) differential on the open interval (a, b), and
3) f(a) = f(b)

then there exists a c such that f'(c) = 0.

Answer 3

A function with the absolute value of a linear term will have a vertex at \((h,k)\) if you can write it as
\[f(x)=a|x-h|+k\]
The function won't be differentiable at the vertex, so check if it's in the interval (0,6).