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

Question

Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.)

f (x) = sin(x),    [0, ]

a.) Yes.

b.) No, because f is not continuous on the closed interval [a, b].

c.) No, because f is not differentiable in the open interval (a, b).

d.) 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 not possible, enter IMPOSSIBLE.)

c=?

Explanation / Answer

f (x) =sin(x)

f (0) =0,f()=0

f(0)=f()

f '(x) = cos(x)

f(a)=f(b)

f is continuous on the closed interval [a, b]

f is differentiable in the open interval (a, b)

so rolls theorem can be applied

f '(c) = cos(c)

f '(c)=0

cos(c)=0

c=/2

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