Tangent to the curve is parallel to the axis is when slope of the tangent is 0. \\\\(\ herefore\\\\) Equation of the curve is\\\\(y=x^3-3x^2-9x+7=0\\\\) ...... \\\\((i)\\\\)\\\\(\ herefore \\dfrac{dy}{dx}=3x^2-6x-9\\\\)Now, the tangent is parallel to x-axis, then slope of the tangent is zero or we can say that \\\\(\\dfrac{dy}{dx}=0\\\\).\\\\(\\Rightarrow 3x^2-6x-9=0\\\\)\\\\(\\Rightarrow 3(x^2-2x-3)=0\\\\)\\\\(\\Rightarrow (x-3)(x+1)=0\\\\)\\\\(\\Rightarrow x=3, -1\\\\)When \\\\(x=3\\\\), then from Eq. \\\\((i),\\\\) we get\\\\(y=(3)^3-(3)\\cdot (3)^2-9\\cdot 3+7\\\\)\\\\(=27-27-27+7=-20\\\\)When \\\\(x =-1,\\\\) then from Eq. \\\\((i),\\\\) we get\\\\(y=(-1)^3-3(-1)^2-9(-1)+7\\\\)\\\\(=-1-3+9+7=12\\\\)Hence, the points at which the tangent is parallel to x-axis are \\\\((3, -20)\\\\) and \\\\((-1, 12)\\\\).