Question

 

Find the maximum and minimum value of  

                      

Solution

Correct option is

 is maximum or minimum according as,  

             

              

  

Using number line rule,  

Which give g’(x) changes sing from –ve to +ve at x = –3, 1  

∴                       local minimum at x = –3, 1 

And local maximum at x = 0 [as changes from +ve to –ve] 

⇒                        g(x) is maximum at x = 0

i.e.,                      gmaximum(0) = 60

and for g(x) to be minimum,

                        

                          

Substituting these values in (i) we get,

  

  

   

                               

 

SIMILAR QUESTIONS

Q1

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

Q2

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:

Q3

 

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

Q4

The function  has a local maximum at x =

Q5

Find the set of critical points of the function  

              

Q6

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

Q7

  

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

Q8

  

Discuss maxima and minima.

 

Q9

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

Q10

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