Application of Derivatives
Show that the function f given by f(x)=tan−1(sinx+cosx),x > 0is always an strictly increasing function in (0,4π).
Find the least value of a such that the function f given by f(x)=x2+ax+1is strictly increasing on (1,2)˙
Prove that the function f given by f(x)=logcosx is strictly decreasing on (0,2π)and strictly increasing on (2π,π)
Find the maximum and minimum values, if any, of the following functions given by
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.
Find the rate of change of the area of a circle with respect to its radius r when(a) r=3cm (b) r=4cm