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Math Help - Critical and Inflection Points of f(x)

  1. #1
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    Post Critical and Inflection Points of f(x)

    f(x) = x + 1/x
    f(x) = x + x^-1

    f'(x) = 1 - x^-2
    f'(x) = 1 -1/x^2

    f"(x) = 2x^-3
    f"(x) = 2/x^3

    To find critical point value of x, I set f'(x) = 0 and solve for x
    To find inflection point value of x, I set f"(x) = 0 and solve for x.
    Unfortunately, this problem doesn't make solving for x very easy.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by confusedagain View Post
    f(x) = x + 1/x
    f(x) = x + x^-1

    f'(x) = 1 - x^-2
    f'(x) = 1 -1/x^2

    f"(x) = 2x^-3
    f"(x) = 2/x^3

    To find critical point value of x, I set f'(x) = 0 and solve for x
    To find inflection point value of x, I set f"(x) = 0 and solve for x.
    Unfortunately, this problem doesn't make solving for x very easy.
    Let us see.

    f'(x) = 1 -1/(x^2)
    Set that to zero,
    0 = 1 -1/(x^2)
    Clear the fractions, multiply both sides by x^2
    0 = x^2 -1
    0 = (x+1)(x-1)
    So,
    x = 1 or (-1) -----------------**

    Or,
    0 = x^2 -1
    x^2 = 1
    x = +,-sqrt(1)
    x = 1 or (-1) --------------same.

    ---------------------------------------------
    f''(x) = 2/(x^3)
    Set that to 0,
    0 = 2/(x^3)
    Clear the fractions, multiply both sides by x^3,
    0 = 2 -------------yeah, right.
    Meaning, there is no inflection point.
    You have and know how to use a graphing calculator? See the graph of f(x) = 1 +1/x. Maybe the graph really does not have an inflection point.
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