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

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Stranger_1973
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Joined: Sun Feb 22, 2009 9:56 pm

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

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?

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

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

Stranger_1973
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Joined: Sun Feb 22, 2009 9:56 pm
So I can use f(6)=69 and f(7)=138 to say that f(a)=100 for 6<a<7?

Martingale
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### Re:

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

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

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

so $a\in(6.5,6.51)$

Stranger_1973
Posts: 21
Joined: Sun Feb 22, 2009 9:56 pm

thanks!