AP CALC. AB

Let h be a function defined for all x≠0 such that h(4)=-3 and the derivative h is given by
h'(x)=(x^2-2)/(x) for all x≠0
a). Find all values of x for which the graph of h has a horizontal tangent, and determine whether h has a local maximum, a local minimum, or neither at each of these values. Justify your answers
b) On what intervals, if any, is the graph of h concave up? Justify your answers

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  1. clearly the tangent is horizontal when

    x^2-2 = 0

    h"(x) = (x^2+2)/x^2

    And you know that f(x) is concave up when f"(x) > 0

    See that graph at

    http://www.wolframalpha.com/input/?i=integral+x+-+2%2Fx

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