Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b].
f(x) = −x2 + 3x, [0, 3]
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 =

Yes, Rolle's theorem can be applied

There is only one value of c such that f'(c) = 0, and this is c = 1.5 (or 3/2 in fraction form)

Step-by-step explanation:

Yes, Rolle's theorem can be applied on this function because the function is continuous in the closed interval (it is a polynomial function) and differentiable  in the open interval, and f(a) = f(b) given that:

Then there must be a c in the open interval for which f'(c) =0

In order to find "c", we derive the function and evaluate it at "c", making the derivative equal zero, to solve for c:

There is a unique answer for c, and that is c = 1.5

true

explanation: