If f(x)=x^3-5x^2+7x-9, use IVT for poly fcns to prove that  TOPIC_SOLVED

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If f(x)=x^3-5x^2+7x-9, use IVT for poly fcns to prove that

Postby Stranger_1973 on Mon Apr 06, 2009 12:38 pm

My ? is on useing the intermediate value thm for polynomial functions. I dont understand how it works. Here is my Problem. If f(x)=x^3-5x^2+7x-9, use the intermediate value theorem for polynomial functions to prove that there is a real number a such that f(a)=100. Help?
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Re: If f(x)=x^3-5x^2+7x-9, use IVT for poly fcns to prove that

Postby Martingale on Mon Apr 06, 2009 1:08 pm

Stranger_1973 wrote:My ? is on useing the intermediate value thm for polynomial functions. I dont understand how it works. Here is my Problem. If f(x)=x^3-5x^2+7x-9, use the intermediate value theorem for polynomial functions to prove that there is a real number a such that f(a)=100. Help?


f(0)=-9 and f(10)=561


since f is a continuous function it must attain all the numbers between -9 and 561 on the interval [0,10] (by the IVT)

since 100 is between -9 and 561 we know that there exists an a in [0,10] such that f(a)=100
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Postby Stranger_1973 on Mon Apr 06, 2009 2:53 pm

So I can use f(6)=69 and f(7)=138 to say that f(a)=100 for 6<a<7?
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Re:

Postby Martingale on Mon Apr 06, 2009 3:01 pm

Stranger_1973 wrote:So I can use f(6)=69 and f(7)=138 to say that f(a)=100 for 6<a<7?


yes
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Re: If f(x)=x^3-5x^2+7x-9, use IVT for poly fcns to prove that  TOPIC_SOLVED

Postby Martingale on Mon Apr 06, 2009 3:03 pm

you could also use f(6.5)=99.875 and f(6.51)=100.563951

so

:wink:
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Re: If f(x)=x^3-5x^2+7x-9, use IVT for poly fcns to prove that

Postby Stranger_1973 on Mon Apr 06, 2009 3:38 pm

thanks! 8-)
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