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Math Help - AP Calculus Multiple Choice Questions- Help!

  1. #1
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    AP Calculus Multiple Choice Questions- Help!

    Hi Everyone, I need some help on a couple of these MC questions for AP Calc AB. Hopefully someone can give me pointers!!

    1) Let f and g be twice differentiable functions such that f'(x) is greater than 0 for all x in the domain of f.
    If h(x)= f(g'(x)) and h'(3)=-2, then at x=3

    A. h is concave down
    B. g is decreasing
    C. f is concave down
    D. g is concave down
    E. f is decreasing

    --------------------------------------------------------------------------

    2. If f is differentiable at x=a, which of the following could be false?

    A. f is continuous at x=a
    B. Limit as x approaches a (f(x)-f(a))/(x-a) Exists
    C. Limit as x approaches a of f(x) exists
    D. f'(a) is defined
    E. f''(a) is defined
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  2. #2
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    Quote Originally Posted by r2d2 View Post
    Hi Everyone, I need some help on a couple of these MC questions for AP Calc AB. Hopefully someone can give me pointers!!

    1) Let f and g be twice differentiable functions such that f'(x) is greater than 0 for all x in the domain of f.
    If h(x)= f(g'(x)) and h'(3)=-2, then at x=3

    h'(x) = f'[g'(x)] g''(x)

    h'(3) = f'[g'(3)] g''(3)

    -2 = (some positive value) g''(3)

    what sign does g''(3) have to have? and what does that tell you about g(x)?

    A. h is concave down
    B. g is decreasing
    C. f is concave down
    D. g is concave down
    E. f is decreasing

    --------------------------------------------------------------------------

    2. If f is differentiable at x=a, which of the following could be false?

    this is really basic ... you need to check your text/notes on what it means for a function to be differentiable at point.

    A. f is continuous at x=a
    B. Limit as x approaches a (f(x)-f(a))/(x-a) Exists
    C. Limit as x approaches a of f(x) exists
    D. f'(a) is defined
    E. f''(a) is defined
    ...
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  3. #3
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    Ok, so for the first question, the answer must be D, because g must be negative, which means g must be concave down


    For the second equation the answer should be A, because a function could be differentiable but not continuous (ex. #/0)
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  4. #4
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    Quote Originally Posted by r2d2 View Post
    Ok, so for the first question, the answer must be D, because g must be negative, which means g must be concave down


    For the second equation the answer should be A, because a function could be differentiable but not continuous (ex. #/0)
    that is incorrect ... differentiabilty implies continuity.

    http://mathforum.org/library/drmath/view/53637.html
    Last edited by skeeter; December 29th 2009 at 05:24 PM. Reason: added link
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