Question

A derivada parcial de segunda ordem f(x,y)= 3 x y - 4 x^2 nos pontos (1,1)

Answer 1

As derivadas de segundo ordem são: $f_{xx}~,~f_{xy}~,~f_{yx}~\&~f_{yy}$

$\textcircled{1}~~f_x=3y-8x\to f_{xx}=-8\\\\ \textcircled{2}~~f_y=3x\to f_{yx}=3=f_{xy}\\ \\ ~~~~~~f_{yy}=0\\ \\ \\ f_{xx}(x,y)=-8~,~f_{xy}(x,y)=3=f_{yx}(x,y)~,~f_{yy}(x,y)=0\\ \\ \hspace*{7cm}\forall (x,y)\in \mathbb R^2$