Application of Derivatives
Find the absolute maximum and minimum values of the function f given by f(x)=cos2x+sinx,x∈[0,π]
Water is dropped at the rate of 2 m3/s into a cone of semi-vertical angle is 45∘ . If the rate at which periphery of water surface changes when the height of the water in the cone is 2m is d. Then the value of 5d is _____ m/sec
Find the equation of tangent and normal to the curve x=(1+t2)2at2,y=(1+t2)2at3 at the point for which t=21˙
Find the equation of the normal to the curve x3+y3=8xy at the point where it meets the curve y2=4x other than the origin.
Discuss the extremum of f(x)=2x3−3x2−12x+5 for x∈[−2,4] and the find the range of f(x) for the given interval.
Find the normal to the curve x=a(1+cosθ),y=asinθahη˙ Prove that it always passes through a fixed point and find that fixed point.