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Feb/Mar 2019 p12 q2
1411
A curve with equation \(y = f(x)\) passes through the points \((0, 2)\) and \((3, -1)\). It is given that \(f'(x) = kx^2 - 2x\), where \(k\) is a constant. Find the value of \(k\).
Solution
To find \(f(x)\), integrate \(f'(x) = kx^2 - 2x\):