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Math Help - Intermediate value theorem

  1. #1
    Super Member 11rdc11's Avatar
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    Intermediate value theorem

    Ok so I know the idea why this is true but how would I prove it.

    If f(x) = x^2 + 10\sin{x} show that therre is a number c such that f(c) = 1000

    I know the function is continous and that its range is to to infinity so it has to equal 1000 at some point but how do I prove it? Thanks
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  2. #2
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    Quote Originally Posted by 11rdc11 View Post
    Ok so I know the idea why this is true but how would I prove it.

    If f(x) = x^2 + 10\sin{x} show that therre is a number c such that f(c) = 1000

    I know the function is continous and that its range is to to infinity so it has to equal 1000 at some point but how do I prove it? Thanks
    If you can prove the statements you said - i.e. that the function is continuous and has an infinite range, then you will have proven your if statement.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by 11rdc11 View Post
    Ok so I know the idea why this is true but how would I prove it.

    If f(x) = x^2 + 10\sin{x} show that therre is a number c such that f(c) = 1000

    I know the function is continous and that its range is to to infinity so it has to equal 1000 at some point but how do I prove it? Thanks
    f(0)=0,f(1001)=101^2+10\sin(1001)\geqslant 1000+10+10\sin(x)\geqslant1000
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