Question

The function f (x) = x (x2 – 4)n (x2 – x + 1), n Ïµ N assumes a local minima at x = 2, then   

Solution

Correct option is

n’ can be any even number

  

  

When we differentiate it less than n times there will be a factor or (x – 2) in every for n1.

  

If we differentiate in n times, only term, with no factor of (x – 2) is one is which (x – 2)n is differention n times

  

  

So if x = 2 is a minima, n must be even. 

                           OR

  

Critical points: x = 2, 0, –2.   

At x = 2; we have a local extremes if  

x = 2 is a double or ever root ⇒ x Ïµ even.

SIMILAR QUESTIONS

Q1

Find the maximum surface area of a cylinder that can be inscribed in a given sphere of radius R 

Q2

Find the semi-vertical angle of the cone of maximum curved surface area that can be inscribed in a given sphere of radius R.

Q3

Find the point on the curve y = x2 which is closest to the point A(0, a).  

Q4

Find the shortest distance between the line y – x = 1 and the curve x = y2.

Q5

Find the vertical angle of right circular some of minimum curved surface that circumscribes in a given sphere.

Q6

 AB > 0, then minimum value of sec A + sec B is equal to   

 

Q8

(x) = x2 – 4 | | and

               

Then (x) has    

 

Q9

If xy = 10, then minimum value of 12x2 + 13y2 is equal to