PLEASE HELP ILL MARK BRAINLIEST

The theorem applies on the given function  .c=3

Step-by-step explanation:

We are given that: on the closed interval: [0,6]

Rolle's Theorem holds if the following conditions are satisfied:

The function must be continuous in [a,b]The function must be differentiable in (a,b)If f(a) = f(b), and there exist c in (a,b) such that

Continuity of function

Since the function is a continuous function, it is continuous everywhere. Therefore, f(x) is continuous in [0,6]

Differentiability of function

The polynomial is differentiable on [0,6] since

Next, we evaluate f(0) and f(6)

Next, we determine if c is in (a,b)

Therefore, c=3 is in (0,6)

Thus, the theorem applies in the given function f(x).c=3