Local minimum point of a cubic located with the first and second derivatives

Let \(\mathrm{f}(x)=2x^3+3x^2-36x\), for \(x\in\mathbb{R}\). The curve \(y=\mathrm{f}(x)\) has exactly one local minimum, at the point \((p,q)\). Find \(p\) and \(q\), justifying that this point is a minimum.[5]