document.write( "Question 760823: find the maximum value of 12sinx-9sin^2x \n" ); document.write( "

Algebra.Com's Answer #462884 by htmentor(1343) $\"\"$ $\"About$

You can put this solution on YOUR website!
Take the derivative and set = 0:
\n" ); document.write( "df/dx = 12cos(x) - 18sin(x)cos(x) = 0
\n" ); document.write( "6cos(x)[2 - 3sin(x)] = 0
\n" ); document.write( "This is satisfied if cos(x) = 0, and sin(x) = 2/3
\n" ); document.write( "cos(x) = 0 -> x = $\"pi\"$ /2
\n" ); document.write( "f( $\"pi\"$ /2) = 12*1 - 9*1 = 3
\n" ); document.write( "This may be a local minimum or a maximum
\n" ); document.write( "Check the other solution:
\n" ); document.write( "12*2/3 - 9*(2/3)^2 = 8 - 4 = 4
\n" ); document.write( "So the maximum value is 4
\n" ); document.write( "The graph is below:
\n" ); document.write( " $\"graph%28300%2C300%2C+-1%2C5%2C-6%2C6%2C+12%2Asin%28x%29+-+9%2A%28sin%28x%29%29%5E2%29\"$ \n" ); document.write( "

\n" );