Determine whether rolle's theorem can be applied to the function f(x) = x(x-2)^2 from 0 to 2

Rolle's theorem can be applies over the interval [0,2] for the given function f(x).

Step-by-step explanation:

We are given the following in the question;

The Rolle's theorem states that is

then, there exist c in the interval (a,b) such that

Condition:

Continuity of f(x)

Since f(x) is a polynomial function, it is continuous i the given interval [0,2].

Differentiability of f(x)

Since f(x) is a polynomial function, it is continuous i the given interval (0,2).

Equality of f(x)

Thus, Rolle's theorem can be applies over the interval [0,2] for the given function f(x).

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