An Inverse Inequality

Calculus Level 2

Let f(x)=x3+ax2+bx+cf(x) = x^3 + ax^2 + bx + c, where a,ba, b, and cc are real numbers. In order for f(x)f(x) to be invertible, aa and bb must be related as: ambnp\dfrac{a^m}{b^n} \leq p , where m,nm, n, and pp are also real numbers.

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

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