document.write( "Question 966543: Use the intermediate value theorem to determine, if possible, whether g(x)=-2x^3-3x+10 has a zero between -1 and 0. If it is not possible to make a determination using this method, state this. \n" ); document.write( "

Algebra.Com's Answer #590748 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"g%28x%29=-2x%5E3-3x%2B10\"$ has a zero between $\"-1\"$ and $\"0\"$ ; \r
\n" ); document.write( "\n" ); document.write( "find the value of $\"g%28-1%29\"$ and $\"g%280%29\"$ , and see where it (if at all) changes sign, that will be the answer\r
\n" ); document.write( "\n" ); document.write( " $\"g%28-1%29=-2%28-1%29%5E3-3%28-1%29%2B10\"$
\n" ); document.write( " $\"g%28-1%29=-2%28-1%29%2B3%2B10\"$
\n" ); document.write( " $\"g%28-1%29=2%2B3%2B10\"$
\n" ); document.write( " $\"g%28-1%29=15\"$ => $\"g%28-1%29%3E0\"$ \r
\n" ); document.write( "\n" ); document.write( "find the value of $\"g%280%29\"$
\n" ); document.write( " $\"g%280%29=-2%280%29%5E3-3%280%29%2B10\"$
\n" ); document.write( " $\"g%280%29=0%2B0%2B10\"$
\n" ); document.write( " $\"g%280%29=10\"$ => $\"g%280%29%3E0%0D%0A%0D%0Aas+you+can+see+there+is+%7B%7B%7Bno\"$ changes in sign, so the answer is $\"g%28x%29=-2x%5E3-3x%2B10\"$ does $\"not\"$ have a zero between $\"-1\"$ and $\"0\"$ \r
\n" ); document.write( "\n" ); document.write( "or, since $\"g%28-1%29+%3E0\"$ and $\"g%280%29+%3E+0\"$ and $\"g\"$ is a polynomial, the Intermediate Value Theorem tells us that $\"g%28x%29+=+0\"$ for some value of $\"x\"$ that is $\"not\"$ between $\"-1\"$ and $\"0\"$ \r
\n" ); document.write( "\n" ); document.write( " let's see it on a graph:\r
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-25%2C+25%2C+-25%2C25%2C+-2x%5E3-3x%2B10%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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