be The Differential Equation Of A Curve And Let P Be The Point Of Maxima Then Number Of Tangents Which Can Be Drawn From P To x2 – y2= a2 is/are:

Then find the value of ‘a’ for which f (x) has local minimum at x = 2.

Discuss maxima and minima.

A cubic f (x) vanishes at x = –2 and has relative maximum/minimum x = –1 and   Find the cubic f (x). 

Find the maximum and minimum value of  

Use the function f (x) = x^1/x, x > 0 to determine the bigger of the two numbers.

The maximum value of 

 then the maximum value of f (θ), is:

The values of ‘K’ for which the point of minimum of the function f (x) = 1 + K²x – x³ satisfy the inequality  belongs to:

The values of a and b for which all the extrema of the function;  is positive and the minimum is at the point  are:

A solid cylinder of height H has a conical portion of same height and radius 1/3^rd of height removed from it. Rain water is falling in the cylinder with rate equal to π times the instantaneous radius of the water surface inside hole, the time after which hole will fill up with water is: