document.write( "Question 1209599: The function D(x) = sin(|x|) is concave up on the interval\r
\n" ); document.write( "\n" ); document.write( "1. ]π, 2π[\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "2. ]-π, 0[\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "3. ]-4π, -3π[\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "4. ]-2π, -π[\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #849651 by ikleyn(52777) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The function D(x) = sin(|x|) is concave up on the interval\r
\n" ); document.write( "\n" ); document.write( "1. ]π, 2π[\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "2. ]-π, 0[\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "3. ]-4π, -3π[\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "4. ]-2π, -π[
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "D(x) = sin(|x|).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The plot of the function D(|x|) is the same as the plot of sin(x) for positive x >= 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The plot of the function D(|x|) at x <= 0 is the mirror reflection about y-axis \r\n" );
document.write( "of the plot of the function sin(x) at x >= 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In positive domain x >= 0,  function sin(x) has the plot concave up in intervals (,).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In particular, function sin(x) has the plot concave up in interval (,), which is option (1).\r\n" );
document.write( "\r\n" );
document.write( "Hence, function D(x) has the plot concave up in the interval (,), which is option (1).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In the negative domain x <= 0, function D(x) = sin(|x|) has the plot concave up in the intervals \r\n" );
document.write( "(,), that are mirror reflections of intervals (,).   (*)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In particular, function sin(|x|) has the plot concave up in interval (,), which is option (4).\r\n" );
document.write( "\r\n" );
document.write( "Hence, function D(x) has the plot concave up in the interval (,), which is option (4).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "But in interval (,), function D(x) is NOT concave up (vice versa, it is concave down).\r\n" );
document.write( "\r\n" );
document.write( "Hence, option (2) is not the solution.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In accordance with (*), function D(x) has the plot concave up in the interval (,), \r\n" );
document.write( "which is option (3).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the intervals where D(x) has the plot concave up are (1), (3), and (4).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  Choices (1), (3) and (4).\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "See the plot of the function D(x) under this link\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "https://www.desmos.com/calculator/cmaszxpgs6\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "https://www.desmos.com/calculator/cmaszxpgs6\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );