document.write( "Question 1192715: A particle is moving in the positive direction, away from the origin along the graph of y = x^2. At what point on the curve are the x and y-coordinates of the particle changing at the same rate? \n" ); document.write( "

Algebra.Com's Answer #824617 by ikleyn(52794) $\"\"$ $\"About$

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\n" ); document.write( "A particle is moving in the positive direction, away from the origin along the graph of y = x^2.
\n" ); document.write( "At what point on the curve are the x and y-coordinates of the particle changing at the same rate?
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document.write( "From  y = x^2,  we have  dy = 2x*dx.    (1)\r\n" );
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document.write( "They want dy = dx, so we put  dy = dx = c  and  substitute this (unknown) value of \"c\" into equation (1)\r\n" );
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document.write( "    c = 2x*c.\r\n" );
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document.write( "Canceling \"c\" in both sides, we get  x =  = 0.5.\r\n" );
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document.write( "So, the  ANSWER  is the point  (x,y) = (0.5,0.25).\r\n" );
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