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
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