Question 1027548
Find the derivative.
{{{df/dx=-2xe^(-x^2/2)}}}
{{{-2xe^(-x^2)=2/e}}}
{{{-2xe^(-x^2)=2e^(-1)}}}
{{{-xe^(-x^2)=e^(-1)}}}
{{{x=-1}}}
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At {{{x=-1}}},{{{y=1/e}}}.
So using the point-slope form of a line,
{{{y-1/e=(2/e)(x-(-1))}}}
{{{y-1/e=(2/e)(x+1)}}}
Substituting (c,0) for (x,y),
{{{0-1/e=(2/e)(c+1)}}}
{{{c+1=-1/2}}}
{{{c=-3/2}}}
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*[illustration fe4.JPG].
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