document.write( "Question 1082177: Find an equation of the tangent line to the graph of
\n" ); document.write( "f(x)= 3sin(2x)-cos(2x) at x= 3(3.14)/ 4 \n" ); document.write( "

Algebra.Com's Answer #696266 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
The slope of the tangent line is equal to the value of the derivative at that point.
\n" ); document.write( "So,
\n" ); document.write( " $\"f=3sin%282x%29-cos%282x%29\"$
\n" ); document.write( " $\"df%2Fdx=6cos%282x%29%2B2sin%282x%29\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"m=6cos%28%283%2F2%29pi%29%2B2sin%28%283%2F2%29pi%29%29\"$
\n" ); document.write( " $\"m=0-2\"$
\n" ); document.write( " $\"m=-2\"$
\n" ); document.write( "At $\"x=%283%2F4%29pi\"$ ,
\n" ); document.write( " $\"f=3sin%28%283%2F2%29pi%29%29-cos%28%283%2F2%29pi%29%29\"$
\n" ); document.write( " $\"f=-3%2B0\"$
\n" ); document.write( " $\"f=-3\"$
\n" ); document.write( "Using the point slope form of a line,
\n" ); document.write( " $\"y-%28-3%29=-2%28x-%283%2F4%29pi%29%29\"$
\n" ); document.write( " $\"y%2B3=-2x%2B%283%2F2%29pi\"$
\n" ); document.write( " $\"y=-2x%2B%283%2F2%29pi-3\"$
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