Mathematics

Problem

Consider the piecewise-defined function

p(x)= \begin{cases} -x^{2}+4x+c,& x\le 2,\\ \ln x + c,& x>2, \end{cases}

where c is a real constant. Determine whether a value of c exists such that p is continuous on

\mathbb{R}

and increasing on its entire domain. Give a brief justification.