document.write( "Question 545163: use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval. please show work.
\n" ); document.write( "can someone please help!!\r
\n" ); document.write( "\n" ); document.write( "f(x)=8x^5-4x^3-9x^2-9; [1,2] \n" ); document.write( "

Algebra.Com's Answer #355539 by KMST(5328) $\"\"$ $\"About$

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The function is a polynomial function, and polynomial functions are continuous. So your intermediate value theorem tells you that between x=1 and x=2, f(x) will take all the values between f(1) and f(2). For any value you pick, between f(1) and f(2), there will be a point x=c, where the function will take that value. (You can always calculate an approximation for that x=c, by trial and error, but it may not be easy, and you may not be able to calculate the exact value).
\n" ); document.write( " $\"f%281%29=8%2A1%5E5-4%2A1%5E3-9%2A1%5E2-9=8-4-9-9=-14%3C0\"$
\n" ); document.write( " $\"f%282%29=8%2A2%5E5-4%2A2%5E3-9%2A2%5E2-9=8%2A32-4%2A8-9%2A4-9=256-32-36-9=179%3E0\"$
\n" ); document.write( "Since $\"f%281%29%3C0\"$ and $\"f%282%29%3E0\"$ , $\"f%281%29%3C0%3Cf%282%29\"$ .
\n" ); document.write( "In other words, zero is between f(1) and f(2).
\n" ); document.write( "So the function has to go through zero at some point in the interval (1,2).
\n" ); document.write( "If f(1) and f(2) were both positive, or both negative, you would not know if the function had a zero in (1,2). \n" ); document.write( "

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