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Which of the following is true for the function f (x) = x + |x| in the interval [-2, 2] for Rolle's theorem?

A.
Continuious and Differentiable
B.
Not - Continuious and Not - Differentiable
C.
Not - Continuious and Differentiable
D.
Continuious and Not -Differentiable

Solution:

Concept:Rolle's Theorem states that if f (x) is a function that satisfies:(i) f (x) is continuous on the closed interval [a, b](ii) f (x) is differentiable on the open interval (a, b)(iii) f (a) = f (b)then there exists a point c in the open interval (a, b) such that f' (c) = 0.Calculation:The fiven function is not differentiable but continous function in the interval [-2, 2].

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