Category: Application of Derivatives

16. A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314

15. Show that height of the cylinder of greatest volume which can be inscribed in a right circular

14. Show that the height of the cylinder of maximum volume that can be inscribed in a sphere

13. Let f be a function defined on [a,b] such that f’(x)>0, for all (xin(a,b)). Then prove that

12. Show that the altitude of the right circular cone of maximum volume that can be inscribed in

11. Find the absolute maximum and minimum values of the function f given by (f(x)=cos^2{x}+sin{x}, xin[0,pi]). Application of

10. Find the points at which the function f given by (f(x)=(x–2)^4 (x+1)^3) has (i) local maxima (ii)

9. A point on the hypotenuse of a triangle is at distance a and b from the sides

8. A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter

7. The sum of the perimeter of a circle and square is k, where k is some constant.