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…
7. The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle. Application…
6. A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8 m3. If building of tank costs Rs 70 per sq metres for…
5. Find the maximum area of an isosceles triangle inscribed in the ellipse (frac{x^2}{a^2}+frac{y^2}{b^2}=1) with its vertex at one end of the major axis. Application of Derivatives Miscellaneous Exercise Previous Next Class 12 Application of Derivatives Miscellaneous Exercise 1. Show…
4. Find the intervals in which the function f given by (fleft(xright)=x^3+frac{1}{x^3},xneq0) is(i) increasing (ii) decreasing. 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…
3. Find the intervals in which the function f given by (fleft(xright)=frac{4sin{x}-2x-xcos{x}}{2+cos{x}}) is (i) increasing (ii) decreasing. 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…
