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1990 Paper 2 Q3
D: 1600.0
B: 1500.0
curve sketching
cubic polynomial
stationary points
discriminant
parametric family
implicit curve
factorisation
Sketch the curves given by \[ y=x^{3}-2bx^{2}+c^{2}x, \] where \(b\) and \(c\) are non-negative, in the cases: \begin{questionparts} \item \(2b < c\sqrt{3}\) \item \(2b=c\sqrt{3}\neq0\) \item \(c\sqrt{3} < 2b < 2c\), \item \(b=c\neq0\) \item \(b > c > 0\), \item \(c=0,b\neq0\) \item \(c=b=0\). \end{questionpart} Sketch also the curves given by \(y^{2}=x^{3}-2bx^{2}+c^{2}x\) in the cases \((i), (v)\) and \((vii)\).
Solution:
