document.write( "Question 182408: Write an equation of a tangent to the curve at a given point:
\n" ); document.write( "y=2x-1/x at P(0.5,-1) \n" ); document.write( "

Algebra.Com's Answer #136897 by Fombitz(32388) $\"\"$ $\"About$

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The slope of the tangent line is the value of the derivative of the function at that point.
\n" ); document.write( "First, find the derivative of the function.
\n" ); document.write( " $\"y=2x-1%2Fx=2x-x%5E%28-1%29\"$
\n" ); document.write( " $\"dy%2Fdx=2-%28-1%29x%5E%28-2%29=2%2B1%2Fx%5E2\"$
\n" ); document.write( "At x=0.5,
\n" ); document.write( " $\"%28dy%2Fdx%29=2%2B1%2F%280.5%29%5E2=6\"$
\n" ); document.write( "Now you have the slope of the line, use the point-slope form of the line,
\n" ); document.write( " $\"y-y%5Bp%5D=m%28x-x%5Bp%5D%29\"$
\n" ); document.write( " $\"y-%28-1%29=6%28x-0.5%29\"$
\n" ); document.write( " $\"y%2B1=6x-3\"$
\n" ); document.write( " $\"y=6x-4\"$
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