Question 2 [25 marks]
a. Determine the first partial derivatives $f_x, f_y, f_{xx}$ and $f_{yy}$ for:
$f(x,y) = \sin(3x) - y^4 e^{6x} + 3yx^2$
Then verify that the conclusion, that is $f_{xy} = f_{yx}$.
[10 marks]
b. A closed rectangular box is to be built with the volume equal to $xyz \ m^3$. The material for the bottom of the box cost RM 1 per $m^2$ while the top and sides cost RM 8 per $m^2$. Evaluate the dimensions (x, y and z) of the box with minimum cost with total volume cost RM 38.
[15 marks]
