Application of Derivatives
The function f(x)=2∣x∣+∣x+2∣=∣∣x∣2∣−2∣x∣∣has a local minimum or a local maximum at x=−2 (b) −32 (c) 2 (d) 32
Prove that the following functions do not have maxima or minima:(i) f (x) = ex (ii) g(x)=logx(iii) h(x)=x3+x2+x+1
Show that the altitude of a right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r/3..
A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top, by cutting off square from each corner and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is maximum ?
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.