Answer
$x=\dfrac{7}{6}$
Work Step by Step
We have: $y=-3x^2+7x-1$
We differentiate both sides with respect to $x$.
$y^{\prime}=\dfrac{d}{dx} [-3x^2+7x-1] \\=-6x+7$
The tangent line to the graph will be horizontal when $ \dfrac{dy}{dx} =0$
Therefore, $-6x +7=0 \implies x=\dfrac{7}{6}$
