Show that the surface area of a closed cuboid with square base and given volume is minimum, when it is a cube.
Then volume of the cubiod
Now, surface area of cubiod
Now differentaiting s w.r.t x we get
for maxima & minima , we have
Now
Again differentiating w.r.t x we get
Thus, s is minimum when
putting in (i) we get
Hence it is a cube since the length, breadth and height of a cube are equal. Hence proved.