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Math Help - [SOLVED] True/False about Derivative Graphing

  1. #1
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    [SOLVED] True/False about Derivative Graphing

    1. If f'(c)=0 and f''(c)>0, then f(x) has a local minimum at c.
    2. If f'(x)<0 for all x in (0,1), then f(x) is decreasing on (0,1).
    3. A continuous function on a closed interval always attains a maximum and a minimum value.
    4. (f(x) + g(x))' = f'(x)+g'(x)
    5. Continuous functions are always differentiable.
    6. If a function has a local maximum at c, then f'(c) exists and is equal to 0.
    7. If f(x)= e^2, then f'(x)=2e

    My answers are:
    1.T
    2.T
    3.T
    4.T
    5.F
    6.T
    7.F

    I know i have exactly one problem wrong, but i can't figure out which one it is.
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  2. #2
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    Quote Originally Posted by biermann33 View Post
    1. If f'(c)=0 and f''(c)>0, then f(x) has a local minimum at c.
    2. If f'(x)<0 for all x in (0,1), then f(x) is decreasing on (0,1).
    3. A continuous function on a closed interval always attains a maximum and a minimum value.
    4. (f(x) + g(x))' = f'(x)+g'(x)
    5. Continuous functions are always differentiable.
    6. If a function has a local maximum at c, then f'(c) exists and is equal to 0.
    7. If f(x)= e^2, then f'(x)=2e

    My answers are:
    1.T
    2.T
    3.T
    4.T
    5.F
    6.T
    7.F

    I know i have exactly one problem wrong, but i can't figure out which one it is.
    recheck #6
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