(a) \(f^{\prime}(x)=3x^2-6x\). At \(x=1\), gradient \(=3-6=-3\).

(b) \(3x(x-2)=0\) gives \(x=0,2\). Turning points \((0,-4),(2,-8)\). Since \(f^{\prime\prime}(x)=6x-6\), they are a maximum and minimum respectively.

(c) A positive cubic rising from bottom left to top right, with both turning points below the \(x\)-axis and the local maximum on the \(y\)-axis.