  We call a smooth function of one variable a degree n pseudopolynomial if its
n-th derivative has no (real) zeros. An n pseudopolynomial is called hyperbolic
if it has exactly n simple zeros. In this short note we describe the necessary
and sufficient conditions on the arrangements of 6 points consisting of 3 zeros
of pseudopolynomials of degree 3, two zeros of their 1st derivatives and 1 zero
of their second derivatives. Besides the standard Rolle's inequalities the
restrictions include additional quadratic inequalities of geometric origin.
  This text is an easy reading accessible for undergraduates. We formulated
also two questions not solved yet.
