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

\text{if=<i>f</i>}
\text{BR=<b>R</b>}
\text{tany=any}

\integer{c=random(1..5)*random(1,-1)}
\integer{t=random(1..5)*random(1,-1)}
\integer{a0=random(1..200)*random(1,-1)}
\integer{a1=random(1..50)*random(1,-1)}
\integer{a2=random(1..10)*random(1,-1)}
\integer{r=random(1..3)*random(1,-1)}
\integer{rd=random(1..4)}
\integer{r0=item(\rd,\r,-(\r)*(\c),(\r)*(\c)^2,0)}
\integer{r1=item(\rd,0,\r,-2*(\r)*(\c),0)}
\integer{r2=item(\rd,0,0,\r,0)}
\integer{b0=-(\c)^3*(\t)+(\a0)-(\r0)}
\integer{b1=3*(\c)^2*(\t)+(\a1)-(\r1)}
\integer{b2=-3*(\c)*(\t)+(\a2)-(\r2)}
\text{F1=htmlmath(\t*x^3 + \b2*x^2 + \b1*x + \b0)}
\text{F2=htmlmath(\a2*x^2 + \a1*x + \a0)}
\integer{rr=random(1,2)}
\text{f1=item(\rr,\F1,\F2)}
\text{f2=item(\rr,\F2,\F1)}
\integer{order=\rd-2}

\statement{Let \if: \BR -> \BR be the function defined by
<p><center><table border=0>
<tr><td nowrap rowspan=2>
\if(x) =
<td nowrap rowspan=2><img src=\imagedir/leftbrace2.gif>
<td nowrap>\f1 <td rowspan=2>&nbsp;&nbsp;&nbsp;&nbsp;
<td nowrap>si x &lt; \c ;
<tr><td nowrap>\f2
<td nowrap>si x <img src=\imagedir/ge.gif> \c .
</table></center> <p>
What is the order of differentiability of \if&nbsp;?
<p>
<b>Instructions/Examples.</b><ul>
<li>Type <tt>3</tt> if \if is differentiable to order 3 but not to order 4.
<li>Type <tt>0</tt> if \if is continuous but not differentiable.
<li>Type <tt>-1</tt> if \if is not continuous.
<li>Type <tt>\tany</tt> if \if is differentiable to any order.
</ul>
}

\answer{Order of differentiability}{\order}

