Local Maxima and Local Minima

Q. A rectangular sheet of metal of length 6 meters and width 2 meters is given. Four equal square are removed from the corners. The sides of this sheet are now turned up to form an open rectangular box. The height of the box (in cm), such that the volume of the box is maximum is

1. 22
2. 25
3. 35
4. 45

Q. If $y=\frac{2lnx}{3x},$ then y has a maximum at x equal to

1. 0
2. 1
3. $\frac{1}{e}$
4. e