document.write( "Question 1027548: A curve is given: y = e^-x^2. Find the point on the curve where the slope of the tangent is 2/e. Label the x-intercept of the tangent line (c,0). Find the x-intercept (c,0) of the tangent line to the curve at that point. \n" ); document.write( "

Algebra.Com's Answer #642766 by Fombitz(32388) $\"\"$ $\"About$

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Find the derivative.
\n" ); document.write( " $\"df%2Fdx=-2xe%5E%28-x%5E2%2F2%29\"$
\n" ); document.write( " $\"-2xe%5E%28-x%5E2%29=2%2Fe\"$
\n" ); document.write( " $\"-2xe%5E%28-x%5E2%29=2e%5E%28-1%29\"$
\n" ); document.write( " $\"-xe%5E%28-x%5E2%29=e%5E%28-1%29\"$
\n" ); document.write( " $\"x=-1\"$
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\n" ); document.write( "At $\"x=-1\"$ , $\"y=1%2Fe\"$ .
\n" ); document.write( "So using the point-slope form of a line,
\n" ); document.write( " $\"y-1%2Fe=%282%2Fe%29%28x-%28-1%29%29\"$
\n" ); document.write( " $\"y-1%2Fe=%282%2Fe%29%28x%2B1%29\"$
\n" ); document.write( "Substituting (c,0) for (x,y),
\n" ); document.write( " $\"0-1%2Fe=%282%2Fe%29%28c%2B1%29\"$
\n" ); document.write( " $\"c%2B1=-1%2F2\"$
\n" ); document.write( " $\"c=-3%2F2\"$
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