Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = −x2 + 6x, [0, 6] Yes, Rolle's Theorem can be applied. No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). No, because f(a) ≠ f(b). If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f '(c) = 0. (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.) c =

Step-by-step explanation:

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

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

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)

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

33

step-by-step explanation: g=6