Consider the function z$($x$,$y$)=5$x$2+1$y$2+0\mathrm{.}9$xy$3$x$+1$y$.$ What is the nature of the critical point of this function? $($Ignore the numbers in brackets.$)$

Question $3$Answer

a$.$

Minimum $(1)$

b$.$

Inflection point $(1)$

c$.$

Maximum $(1)$

d$.$

Test is inconclusive $(1)$