State why Rolle's Theorem does not apply to the function f(x) = on the interval [-2, 0]

a) f is not continuous on [-2,0]

b) f(-2) not equal f(0)

c) f is not differentiable at x = -1

d) Both a and c

e) None of these

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- Jul 26th 2007, 08:36 AMSamanthaRolle's Theorem
State why Rolle's Theorem does not apply to the function f(x) = on the interval [-2, 0]

a) f is not continuous on [-2,0]

b) f(-2) not equal f(0)

c) f is not differentiable at x = -1

d) Both a and c

e) None of these - Jul 26th 2007, 08:42 AMPlato
What is the domain of the function

*f*? - Jul 26th 2007, 08:46 AMtopsquark
Rolle's theorem doesn't apply because the function is not continuous on [-2, 0]. (There is a discontinuity at x = -1.)

a) I already said why this is true.

b) f(-2)*does*equal f(0).

and

c) f(x) is, in fact, not differentiable at x = -1 because the function does not exist there.

As both a) and c) are true, and Rolle's theorem depends on them being true (and f(-2) = f(0) to boot) the answer should be d).

-Dan