Answer:
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