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Math Help - Rolle's Theorem

  1. #1
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    Rolle's Theorem

    State why Rolle's Theorem does not apply to the function f(x) = \frac {2} {(x+1)^2} 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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    What is the domain of the function f ?
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    Quote Originally Posted by Samantha View Post
    State why Rolle's Theorem does not apply to the function f(x) = \frac {2} {(x+1)^2} 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).
    f(-2) = \frac{2}{(-2 + 1)^2} = \frac{2}{(-1)^2} = \frac{2}{1} = 2
    and
    f(0) = \frac{2}{(0 + 1)^2} = \frac{2}{(1)^2} = \frac{2}{1} = 2

    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
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