Download bdd and cbdd and the step by step of understanding and of them also.Q: What is a property of a small portion of a piecewise function? Given a piecewise-defined function $f$ with $n$ pieces on intervals $[a_1,b_1],\cdots,[a_n,b_n]$ respectively: $$f(x)=\begin{cases} c_1, & \text{x\in [a_1,b_1]}\\ c_2, & \text{x\in [a_2,b_2]}\\ \cdots\\ c_n, & \text{x\in [a_n,b_n]}\\ \end{cases}$$ What we can say about the properties of a small portion $[a_1,b_1]$ of the function? What about $[a_2,b_2]$? What is the relationship between this small portion and the whole function? A: You can not say anything about the properties of a part of $f$. But you can say that the derivative of $f$ vanishes at a point $a_k$. Without any further assumptions (eg. $f$ is continuous at $a_1$) the derivative of $f$ at $a_1$ is $f'(a_1)$. By induction this says that $f'(x)$ is undefined at the points $a_k$. The converse holds also: If the derivative of $f$ does vanish at $a_1$, then $f$ is analytic at $a_1$. A typical example of this type of result are $f(x)=0$ where $f'(x)=0$ at $a_1$, which is the same as $f$ being analytic at $a_1$. the rest of the attributes. :returns: The next definition stage of the operation. :rtype: :class:oefn.l5d.op_def_stage.OpDefStage 1cdb36666d