Higher Engineering Mathematics

364 DIFFERENTIAL CALCULUS

5. Locate the stationary points on the surface

f(x,y)= 2 x^3 + 2 y^3 − 6 x− 24 y+ 16

and determine their nature.

[

Minimum at (1, 2),

maximum at (−1,−2),

saddle points at (1,−2) and (−1, 2)

]

6. A large marquee is to be made in the form
   of a rectangular box-like shape with canvas
   covering on the top, back and sides. Deter-
   mine the minimum surface area of canvas
   necessary if the volume of the marquee is to
   the 250 m^3. [150 m^2 ]