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) = x4/5 5,    [32, 32]

a.) Yes, Rolle's Theorem can be applied.

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) = x4/5 5

f '(x) = (4/5)x-1/5

f '(x) = 4/(5x1/5)

f '(x) is not defined at x =0 which lies in the interval [-32,32]

so rolls theorem cannot be applied

No, because f is not differentiable in the open interval (-32, 32).

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

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