given by f ( x ) = ( x – ) ( x + ) has (i) local maxima (ii) local minima (iii) point of inflexion . Find the absolute maximum and minimum values of the function f given by f ( x ) = cos x + sin x , x ∈ [ , π ] . Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is r . .
Let f be a function defined on [ a , b ] such that f ′ ( x ) > , for all x ∈ ( a , b ). Then prove that f is an increasing function on ( a , b ). . Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is 2R .
Also find the maximum volume. . 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 tan h α . .
A cylindrical tank of radius m is being filled with wheat at the rate of cubic metre per hour. Then the depth of the wheat is increasing at the rate of (A) m/h (B) . m/h (C) . m/h (D) .