Find the coordinates of the point of inflection of the curve f(x) `=e^(-x^(2))

Explanation

To find the coordinates of the point of inflection of the curve given by the function \( f(x) = e^{-x^2} \), we need to follow these steps:

### Step 1: Find the first derivative \( f'(x) \)
To find the first derivative, we will use the chain rule. The derivative of \( e^{u} \) is \( e^{u} \cdot u' \), where \( u = -x^2 \).

\[ f'(x) = \frac{d}{dx}(e^{-x^2}) = e^{-x^2} \cdot \frac{d}{dx}(-x^2) = e^{-x^2} \cdot (-2x) = -2x e^{-x^2} \]
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