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Math Help - Equilibrium point

  1. #1
    Len
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    Equilibrium point

    Let f(y) be a continuous function:

    Suppose that f(-10)>0 and f(10)<0, show that there is a equilibrium point for dy/dt=f(y) between y=-10 and y=10.

    Just realized I posted this is in the wrong section, should be in Differential Equations, sorry.
    Last edited by Len; January 26th 2010 at 11:33 AM.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    Recall an equillibrium solution occurs where f(y) = 0 for dy/dt = f(y)


    By the Intermediate Value Theorem if f(10) < 0 and f(-10) > 0

    Then f has a zero between -10 and 10
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  3. #3
    Len
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    Quote Originally Posted by Calculus26 View Post
    Recall an equillibrium solution occurs where f(y) = 0 for dy/dt = f(y)


    By the Intermediate Value Theorem if f(10) < 0 and f(-10) > 0

    Then f has a zero between -10 and 10
    Thanks, I didn't even think to apply that.

    The intermediate value theorem states the following: If the function y = f(x) is continuous on the interval [a, b], and u is a number between f(a) and f(b), then there is a c ∈ [a, b] such that f(c) = u.

    For anyone else who reads.
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