\title{Non-differentiable inverse}
\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{x0=x<sub>0</sub>}
\real{a=randint(5..20)*random(-1,1)/10}
\real{c3=randint(1..10)*random(-1,1)}
\real{c2=-3*(\c3)*(\a)}
\real{c1=3*(\c3)*(\a)^2}
\real{c0=randint(5..100)*random(-1,1)/10}
\function{f=\c3*x^3+\c2*x^2+\c1*x+\c0}
\text{ft=htmlmath(\f)}
\real{v0=evalue(\f,x=\a)}

\statement{The function \if: \BR -> \BR defined by
<p><center>
\if(x)&nbsp;=&nbsp;\ft
</center> <p>
is bijective, but there is a point
\x0&nbsp;<img src=\imagedir/in.gif>&nbsp;\BR
such that
the inverse function \if<sup>-1</sup>(x) is not differentiable on \x0.
Find \x0.
}

\answer{\x0}{\v0}

