How many stationary points does the curve $y = x^{4} - 4 x^{3}$ have?

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What is the local maximum value of $f (x) = x^{3} - 6 x^{2} + 9 x$ ?
What is the gradient of the curve $y = x^{3} - 3 x$ at the point where $x = 2$ ?
The tangent to $y = x^{2}$ at the point where $x = 3$ crosses the $x$ -axis at $(p, 0)$ . What is $p$ ?
The normal to the curve $y = x^{2} + 1$ at the point $(1, 2)$ crosses the $y$ -axis at $(0, c)$ . What is $c$ ?
The curve $y = x^{3} + a x^{2} + b$ has a stationary point at $x = 2$ . What is $a$ ?
The function $f (x) = x^{3} - 3 x^{2} + k$ has a local minimum value of $0$ . What is $k$ ?