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:
At point of maxima f’(x) = 0 and f’’(x) < 0
lies outside x2 – y2 = a2.
∴ Two normals can be drawn.
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) = x1/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 1/3rd 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: