E-DE03 · Recover the entire cubic
\(f(x)=ax^3+bx^2+cx+4\). It is given that \(f^{\prime}(1)=0\), \(f^{\prime}(2)=9\), and \(f^{\prime\prime}(1)=6\).
Express \(f^{\prime}(x)\) and \(f^{\prime\prime}(x)\) in terms of the constants.
Find a, b and c.
Find and classify both stationary points of the recovered curve.
Complete-answer checking, worked solutions and indicative written criteria.
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