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Consider the following function and closed interval. f ( x ) = ( x 5 ) ( x 6 ) ( x 8 ) ,

Consider the following function and closed interval.
f(x)=(x 5)(x 6)(x 8),[5,8]
Is f continuous on the closed interval [5,8]?
YesNo
If f is differentiable on the open interval (5,8), find
f'(x).
(If it is not differentiable on the open interval, enter DNE.)
f'(x)=
3x238x+118
Find f(5) and f(8).
f(5)= f(8)=
Determine whether Rolle's Theorem can be applied to f on the closed interval
[a, b].
(Select all that apply.)
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 =
5.451,7.215

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