Question

Verify Rolle's theorem for the following functions f(x) = 1 - |x - 1| on [0,2] ​

Answer 1

Answer:

Since the given function is not differentiable at x = 1 ∈ (0,2) , Rolle's theorem is not applicable  

Step-by-step explanation:

Rolle's theorem :

If a function f with domain [a , b] is such that it is

(1) continuous in [a , b]

(2) derivable in (a , b)

(3) f(a) = f(b) , then there exist c ∈ (a , b) s.t f'(c) = 0

Here the given function f(x) = 1 - |x - 1| is not differentiable at x = 1 ∈ (0,2)

Hence Rolle's theorem is not applicable in this case.

Answer 2

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