Question

  

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

Solution

Correct option is

a ≤ –1    or    a ≥ 10

We have   

                            

(x) has local minima at x = 2.   

Since, f (x) = 2x – 3 for x ≥ 2 (is strictly increasing)   

  

                      

                      

                       

                    (a + 1)(a – 10) ≥ 0   

                   a ≤ –1    or    a ≥ 10.

SIMILAR QUESTIONS

Q1

Find the critical points for f (x) = (x – 2)2/3 (2x + 1).

Q2

 

Find all the values of a for which the function possess critical points.

 

Q3

 

Using calculus, find the order relation between x and tan-1x when x Ïµ [0, ∞). 

Q4

Using calculus, find the order relation between x and tan-1x when  

Q5

The set of all values of ‘b’ for which the function (x) = (b2 – 3b + 2) (cos2x – sin2x) + (b – 1) x + sin 2 does not possesses stationary points is:

Q6

 

Find the local maximum and local minimum of (x) = x3 + 3x in [–2, 4].

Q7

The function  has a local maximum at x =

Q8

Find the set of critical points of the function  

              

Q9

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

Q10

  

Discuss maxima and minima.