Given, demand function is D = 100 - $"p"^2/2$
$"dD"/"dp" = 0 - "2p"/2 = -"p"$
$eta = (-"p")/"D" * "dD"/"dp"$
$eta = (-"p")/(100 - "p"^2/2) * (- "p")$
$= "p"^2/((200 - "p"^2)/2)$
$eta = "2p"^2/(200 - "p"^2)$
When p = 6,
$eta = (2(6)^2)/(200 - (6)^2) = 72/164 = 18/41$
elasticity of demand at p = 6 is $18/41$
Here, > 0
The demand is inelastic.
