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Finding Second and Third Derivative from Graph

  1. Feb 21, 2017 #1
    1. The problem statement, all variables and given/known data

    The problem asks to find g'(2), g''(2), and g'''(4).

    2. Relevant equations and attempt at solution

    The derivative of g(x) is just the function f(x). So g'(2) = f(2) = -2.

    I'm not sure how to find g''(2) and g'''(4).
    I understand that g''(2) is f'(2), but how do I find the derivative of f from this graph? Same question for g'''(4) = f''(4).

    Attached Files:

  2. jcsd
  3. Feb 21, 2017 #2


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    2017 Award

    Staff: Mentor

    Why don't you simply compute ##g(x)\,##? Just integrate for ##1 \leq x \leq 2## then for ##2 \leq x \leq 3\, , \,3\leq x \leq 4## and ##4\leq x \leq 5\,.## After this you could draw this function and see whether and where it is differentiable and what the values are.
  4. Feb 21, 2017 #3

    Ray Vickson

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    The graph gives a complete and exact description of the function ##f(x)##. You just need to translate the given information into formulas.
  5. Feb 21, 2017 #4
    I think I'm getting somewhere...
    g''(2) = f'(2) is DNE because of the sharp curve, where the tangent line is a vertical line.
    g'''(4) = f''(4) is 0 because the first derivative is a constant and the second is 0.
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