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determine whether Rolle\'s Theorem can be applied to f on the closed interval [a

ID: 2868801 • Letter: D

Question

determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. if Rolle's Theorem can be applied, find all values of c in the open interval (a,b) such that f'(c)=0. if Rolle's Theorem cannot be applied explain why not completely.
f(x)=sinx [0,2pi] determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. if Rolle's Theorem can be applied, find all values of c in the open interval (a,b) such that f'(c)=0. if Rolle's Theorem cannot be applied explain why not completely.
f(x)=sinx [0,2pi]
f(x)=sinx [0,2pi]

Explanation / Answer

f(a)=f(0)= sin 0 =0

f(b)=f(2pi)= sin 2pi =0

f(a)=f(b) so rolls theorem can be applied

f'(x)=cosx

f'(c)=0

==> cos c =0

cos c is interval[0,2pi] when c =pi/2, 3pi/2