SupremeCookie said: The gradient of the curve is $\frac{dy}{dx}$. Find it. The gradient of the curve is minimized when $\frac{d^2y}{dx^2}=0$ Click to expand... Alternatively, Spoiler $\frac{dy}{dx}=6x^2-12x+8$ a parabola that concaves up, thus the minimum is at the vertex $\frac{-b}{2a}=\frac{-(-12)}{2\times6}=1$ and $\left . \dfrac{dy}{dx}\right |_{x=1} = 2$ Therefore, $\frac{dy}{dx} \ge 2$