Question

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

Solution

Correct option is

  

  

  

∴ Using number line rule for (x + 2) (x + 3) as shown above.  

             

Now consider,  

               

               

              

or maximum/minimum let f’(x) = 0,  

   

   

  

∴ (x) is maximum at x = x1, and (x) is minimum at x = x2.  

  

  

  

SIMILAR QUESTIONS

Q1

Find the set of critical points of the function  

              

Q2

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

Q3

  

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

Q4

  

Discuss maxima and minima.

 

Q5

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

Q6

 

Find the maximum and minimum value of  

                      

Q7

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

Q8

 

The maximum value of 

Q9

 then the maximum value of (θ), is:

Q10

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