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Math Help - Finding critical points and inflections

  1. #1
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    Finding critical points and inflections

    For positive constants A and B, the force between two atoms in a molecule is given by the following equation, where r > 0 is the distance between the atoms.

    f(r)=-(A/r^2)+(B/r^3)

    (a) Find f '(r)

    (b) Find the critical point for f(r).

    (c) Classify the critical point as a minimum, maximum, or neither.

    (d) Find the inflection point for f(r).

    I found f'(r) and I got the critical point to be (3b/2a), but am not so sure about that.

    Thanks in advance,

    Tyler
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  2. #2
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    Yep, f'(r) = 0 if and only if r= 3B/2A
    Then for c you need to find f''(r) and when you test the critical point in the second derivative: if f''(r) > 0 the it's a Local min. or if f''(r) < 0 then it's a local max.
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