document.write( "Question 1184174: Can we apply role's theorem in the intervals [-3, 3] and [-2, 2] for the function g(x) = πx? \n" ); document.write( "

Algebra.Com's Answer #814712 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"g%28x%29+=+pi%2Ax\"$ in the intervals [ $\"-3\"$ , $\"3\"$ ]\r
\n" ); document.write( "\n" ); document.write( " $\"g%28x%29+=+pi%2Ax\"$ is continuous and differentiable on [ $\"-3\"$ , $\"3\"$ ]
\n" ); document.write( " $\"g%28-3%29+=+pi%2A%28-3%29=-3pi\"$
\n" ); document.write( " $\"g%283%29+=+pi%2A%283%29=3pi\"$
\n" ); document.write( " $\"g\"$ ' $\"%28x%29+=+pi\"$
\n" ); document.write( "=> since $\"g%28-3%29+%3C%3Eg%283%29\"$ , role's theorem cannot be applied\r
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\n" ); document.write( "\n" ); document.write( " $\"g%28x%29+=+pi%2Ax\"$
\n" ); document.write( "is continuous and differentiable on [ $\"-2\"$ , $\"2\"$ ]
\n" ); document.write( " $\"g%28-2%29+=+pi%2A%28-2%29=-2pi\"$
\n" ); document.write( " $\"g%282%29+=+pi%2A%282%29=2pi\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"g\"$ ' $\"%28x%29+=+pi\"$ \r
\n" ); document.write( "\n" ); document.write( "=> since $\"g%28-2%29+%3C%3Eg%282%29+\"$ , role's theorem cannot be applied\r
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