\title{Continuity of derivative II}
\language{en}
\range{-0.9..0.9}
\author{Gang XIAO}
\email{xiao@unice.fr}
\computeanswer{yes}
\format{html}
\precision{10000}

\text{tyes=Yes}
\text{tno=No}
\text{if=<i>f</i>}
\text{BR=<b>R</b>}
\text{fp=\if&nbsp;<tt>'</tt>}
\text{in=&nbsp;<img src=\imagedir/in.gif>&nbsp;}
\text{tone=random(increasing, decreasing,
	strictly increasing, strictly decreasing)}

\text{condlist=\if(x) is bounded,
	\fp(x) is bounded,
	\if is \tone,
	\fp is \tone,
	lim<sub>x->x<sub>0</sub></sub>\if(x) exists for any x<sub>0</sub>\in\BR,
	
	lim<sub>x->x<sub>0</sub></sub>\fp(x) exists for any x<sub>0</sub>\in\BR,
	|\if(x)-\if(y)|&nbsp;&lt;&nbsp;|x-y| for all x and y\in\BR,
	|\fp(x)-\fp(y)|&nbsp;&lt;&nbsp;|x-y| for all x and y\in\BR,
	\if is \tone and bounded,
	\fp is \tone and bounded
}
\text{goodlist=\tno,\tno,\tno,\tyes,\tno,
	\tyes,\tno,\tyes,\tno,\tyes
}
\integer{n=random(1..items(\condlist))}
\text{cond=item(\n,\condlist)}
\text{good=item(\n,\goodlist)}

\statement{Let \if: \BR -> \BR be a continuous function. Suppose that the
derivative \fp(x) exists for any point x\in\BR.
<p>
If furthermore \cond,
is the derivative function
\fp: \BR -> \BR always continuous?
}

\choice{Reply}{\good}{\tyes,\tno}

