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Math Help - Calculus...check my work please

  1. #1
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    Calculus...check my work please

    http://www.math.rutgers.edu/~greenfi...fstuff/w3N.pdf

    To that problem

    I have

    a) increasing for [0,C) and (D,E] since f'(x) is positive there, and so, decreasing for (C,D). Local extrema would just be C as a local max? (Not sure though since it isn't continuous)

    b) concave up=f''(x)>0 for [0,A)U[B,C)U(C,E] and concave down only for (A,B) since that is the only place where slope is negative. So point of inflection would be both A and B?

    c) Not sure how I could draw the graph....Do I just draw anything that fits those specification or how can I know where things start and stop?
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  2. #2
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    Quote Originally Posted by zhupolongjoe View Post
    http://www.math.rutgers.edu/~greenfi...fstuff/w3N.pdf

    To that problem

    I have

    a) increasing for [0,C) and (D,E] since f'(x) is positive there, and so, decreasing for (C,D). Local extrema would just be C as a local max? (Not sure though since it isn't continuous) Yes, local max at C. But what happens at D?

    b) concave up=f''(x)>0 for [0,A)U[B,C)U(C,E] and concave down only for (A,B) since that is the only place where slope is negative. So point of inflection would be both A and B? Yes.

    c) Not sure how I could draw the graph....Do I just draw anything that fits those specifications Yes!
    or how can I know where things start and stop? The only information you have cincerns the derivative. So f can only be determined up to a constant (like a constant of integration).
    ..
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  3. #3
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    thanks and so D-local min
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