Given the above graph of the derivative, f '(x), of a function f(x),
    (a)    Name five different, interesting characteristics of the original function f.
    (b)    Draw f '' and f '''.

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Solution:

(a)    There are numerous solutions, but here are five samples--they don't even scratch the surface of concavity, but you can definitely get some cancavity information from the graph!
        *   f is increasing on .
        *   f is decreasing on .
        *   f has four inflection points, occurring at x = -3, -1, 2, and 6.
        *   f has a local maximum (or relative maximum) at x = 0.
        *   f has a relative (local) minimum at x = 4.

(b) 

Calculus II (BC): Integrating by Partial Fractions

Try this integration problem on for size:

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Solution:

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