Application of Derivatives
Find the absolute maximum and minimum values of a function f given by f(x)=2x3−15x2+36x+1on the interval (3.02),[1,5].
The pressure p and volume V of gas are connected by the relation, pV1/4=k, where k is a constant. Find the percentage increase in the pressure, corresponding to a diminution of 0.5% in the volume.
Find a point of the curve y=x3, where the tangent to the curve is parallel to the chord joining the points (1,1) and (3,27).
A man is moving away from a 40 m high tower at a speed of 2 m/s. Find the rate at which the angle of elevation of the top of the tower is changing when he is at a distance of 30 metres from the foot of the tower. Assume that the eye of the man is 1.6 m from the ground.