# Piecewise Functions - 3

Calculus Level 5

Let a function $$f : \mathbb{R} \rightarrow \mathbb{R}$$ be defined as:

$f(x) = \begin{cases} \sin x, & \text{if } a < x \leq b \\ |x - c | - d, & \text{if } x \leq a \text{ or } x > b. \end{cases}$

It is given:

• $$a, b, c, d$$ are real numbers
• $$f$$ is a differentiable function for all real values of $$x$$

Find the minimum possible value of $$\lvert \lfloor a + b + c + d \rfloor \rvert$$.

Details and assumptions

$$\lfloor \cdot \rfloor$$ is the floor function

This problem is part of the set - Piecewise-defined Functions

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