Category class 12

16. A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of(A) (1  m^3/h) (B) (0.1   m^3/h)…

15. Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle α is one-third that of the cone and the greatest volume of cylinder is…

14. Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (frac{2R}{sqrt3}). Also find the maximum volume. Application of Derivatives Miscellaneous Exercise Previous Next Class 12 Application of Derivatives…

13. Let f be a function defined on [a,b] such that f’(x)>0, for all (xin(a,b)). Then prove that f is an increasing function on (a,b). Application of Derivatives Miscellaneous Exercise Previous Next Class 12 Application of Derivatives Miscellaneous Exercise 1.…

12. Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is (frac{4r}{3}). Application of Derivatives Miscellaneous Exercise Previous Next Class 12 Application of Derivatives Miscellaneous Exercise 1.…

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 Derivatives Miscellaneous Exercise Previous Next Class 12 Application of Derivatives Miscellaneous Exercise 1. Show that the function given by (fleft(xright)=frac{log{x}}{x}) has maximum…

10. Find the points at which the function f given by (f(x)=(x–2)^4 (x+1)^3) has (i) local maxima (ii) local minima (iii) point of inflexion Application of Derivatives Miscellaneous Exercise Previous Next Class 12 Application of Derivatives Miscellaneous Exercise 1. Show…

9. A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the maximum length of the hypotenuse is ((a^{2/3}+b^{2/3} )^{3/2}). Application of Derivatives Miscellaneous Exercise Previous Next Class…

8. A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening. Application of…