Anonymous
Anonymous asked in Science & MathematicsMathematics · 9 years ago

What should be the graph of the the function with these given properties?

f(5) = 12, f '(x) <0 for x < 0 and x > 5, f '(x) >0 for 0 <x < 5, f '(5) = 0, f(0) and f '(0) do not exist

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  • s k
    Lv 7
    9 years ago
    Favorite Answer

    f'(5) = 0, f'(0) DNE => f'(x) = a(x - 5)/x

    f'(1) = -4a > 0, let a = -1.

    f'(x) = (5 - x)/x

    f'(-1) = (5 + 1)/(-1) = -6 < 0

    So we're good.

    Then f(x) = ∫f'(x)dx

    = ∫(5/x - 1)dx = 5ln|x| - x + C.

    f(5) = 12 = 5ln(5) - 5 + C

    17 - 5ln(5) = C

    So f(x) = 5ln|x| - x + 17 - 5ln(5).

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