# The Greatest Sin

**Calculus**Level 4

Let \(f(x) \) denote the function of the expression above. If the greatest possible value of \(f(x)\) can be represented by the form \[\left(\dfrac{\sqrt{c}-b}{a}\right)^{\large\frac{1}{a}} \cdot e^{\stackrel{\large\frac{\sqrt{c}-b}{a}}{}}\]

Where \(a,b,c\) are constants and \(e\approx 2.7183...\) (Euler's constant) and \(a,b,c\) are integers. Find \(a+b+c\).