366 Higher Engineering Mathematics
4. Determine the stationary points of the surface
f (x, y) = x
3
− 6x
2
− y
2 .
Maximum at (0, 0),
saddle point at (4, 0)
5. Locate the stationary points on the surface
f (x, y) = 2x
3
+ 2y
3
− 6x − 24y + 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. Determine
the minimum surface area of canvas necessary
if the volume of the marquee is to the 250 m 3 .
[150 m 2 ]