[tex]f(x) = -x^2+px+q \\\\ f'(x) = -2x+p \\ \\ \\f_{max} = f(-1)\,\,\Leftrightarrow\,\,f'(-1) = 0\\ \\ \Rightarrow f(-1) = 4\quad \wedge\quad f'(-1) = 0 \\ \Rightarrow -1-p+q= 4\quad \wedge \quad 2+p = 0 \\ \Rightarrow q = 5+p\quad \wedge \quad p = -2\\\\\Rightarrow \boxed{q = 3}\quad \wedge \quad \boxed{p = -2}[/tex]
