# An Inverse Inequality

Calculus Level 2

Let $$f(x) = x^3 + ax^2 + bx + c$$, where $$a, b$$, and $$c$$ are real numbers. In order for $$f(x)$$ to be invertible, $$a$$ and $$b$$ must be related as: $$\dfrac{a^m}{b^n} \leq p$$, where $$m, n$$, and $$p$$ are also real numbers.

Find the mimimum value of $$m + n + p$$.

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