Hello - I have been messing around with this problem for a while, please help.
I actually know the solution, but cannot reach it on paper:
Find where the slope of the tangent to the curve e^(-x^2) is equal to 2/e
The Attempt at a Solution
d/dx e^(-x^2) = e^(-x^2) * d/dx -x^2 = -2xe^(-x^2)
Set: -2xe^(-x^2) = 2/e
e^(-x^2 + 1) = -1/x
(e^(-x^2 + 1))^-1 = (-1/x)^-1
e^(x^2-1) = -x
At this point I can see that the only possible solution is x = -1, yet cannot actually reach that conclusion on paper. It seems like I'm missing something ridiculously simple.
Any help greatly appreciated!