SOLUTION: 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

Algebra ->  Rational-functions -> SOLUTION: 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       Log On


   

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.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the derivative.
df%2Fdx=-2xe%5E%28-x%5E2%2F2%29
-2xe%5E%28-x%5E2%29=2%2Fe
-2xe%5E%28-x%5E2%29=2e%5E%28-1%29
-xe%5E%28-x%5E2%29=e%5E%28-1%29
x=-1
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At x=-1,y=1%2Fe.
So using the point-slope form of a line,
y-1%2Fe=%282%2Fe%29%28x-%28-1%29%29
y-1%2Fe=%282%2Fe%29%28x%2B1%29
Substituting (c,0) for (x,y),
0-1%2Fe=%282%2Fe%29%28c%2B1%29
c%2B1=-1%2F2
c=-3%2F2
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