$$$
\left.\frac{\partial f(c)}{\partial c}\right|_{c=0} = 0
$$$

$$$
\left.\frac{\partial f(c)}{\partial c}\right|_{c=1} = 0
$$$

$$$
\left.\frac{\partial^2 f(c)}{\partial c^2}\right|_{c=\sigma} = 0
$$$

$$$
\left.\frac{\partial^2 f(c)}{\partial c^2}\right|_{c=1-\sigma} = 0
$$$