# Let's mimimize

Calculus Level 4

If the curve $$f(x)=2{ x }^{ 3 }+a{ x }^{ 2 }+bx$$, where $$a$$ and $$b$$ are positive integers, cuts the $$x$$-axis at three distinct points. Then find the minimum value of $$a +b$$.

Bonus: Also find all $$f(x)$$ for which $$a+b$$ is minimum.

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