Module 4 : Local / Global Maximum / Minimum and Curve Sketching
Lecture 11 : Absolute Maximum / Minimum [Section 11.1]
PRACTICE EXERCISES
1.
Find the global maximum and the global minimum of on , where
.
2.
Analyze the function for points of absolute maximum/minimum:
3.
Find points of absolute maximum and absolute minimum of the function
in the intervals .
4.
A window is to be made in the form of a rectangle surmounted by a semicircular portion with diameter equal to the
the base of the rectangle. The rectangular portion is to be of clear glass and the semicircular portion is to be of colored glass admitting only half as much light per square foot as the clear glass. If the total perimeter of the window frame is to be feet, find the dimensions of the window which will admit the maximum light.
5.
The cost of per hour of fuel to run a truck is Rupees, where is the speed in km/hour. There is an additional
cost of Rs.1000/- per hour to run the truck. What should be the speed to minimize the cost per km.
6.
Find the ratio of the height to the diameter of the base of cylinder of maximum volume that can be inscribed in a
on 
, where 
. 
for points of absolute maximum/minimum: 
. 
feet, find the dimensions of the window which will admit the maximum light. 
Rupees, where 
is the speed in km/hour. There is an additional
. 
