document.write( "Question 1142316: Calculus Question\r
\n" ); document.write( "\n" ); document.write( "Use the Intermediate Value Theorem and Rolle's Theorem to determine that $\"+f%28x%29=x%5E7%2B4x%5E5%2B3x%2B5+\"$ has exactly one real root between -1 and 0. \n" ); document.write( "

Algebra.Com's Answer #763585 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If a function

is continuous on the closed interval

and has values

and

at each end of the domain interval, then the function takes on any value in the interval

at some point in the domain interval.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "All polynomial functions with real coefficients are everywhere continuous.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "is a polynomial function with real coefficients and is therefore everywhere continuous and is therefore continuous on the interval

.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Therefore

has any value in the interval

for some

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

therefore

\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "John
\n" ); document.write( "

\n" ); document.write( "My calculator said it, I believe it, that settles it
\n" ); document.write( "

\n" ); document.write( "

\n" );