Answer
$ x=0$
Work Step by Step
We have: $y=e^{x^2}$
We differentiate both sides with respect to $x$.
$y^{\prime}=\dfrac{d}{dx} [e^{x^2}] \\=2xe^{x^2}$
The tangent line to the graph will be horizontal when $ \dfrac{dy}{dx} =0$
Therefore, $2xe^{x^2}=0 \implies x=0$
