Question

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

Solution

Correct option is

For  extrema, f’(x) = 0  

   

  

  

   

So their arises two cases as:

Case I: At a = 3, if function attains minimum and is positive.

   

      

  

Case II: at a = –2, if function attains minimum and is positive. 

  

   

  

   

SIMILAR QUESTIONS

Q1

Let (x) = sin x – x on [0, π/2], find local maximum and local minimum.

Q2

  

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

Q3

  

Discuss maxima and minima.

 

Q4

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

Q5

 

Find the maximum and minimum value of  

                      

Q6

Use the function (x) = x1/xx > 0 to determine the bigger of the two numbers.

Q7

 

The maximum value of 

Q8

 then the maximum value of (θ), is:

Q9

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

Q10

 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 – y2a2 is/are: