Question

The function f (x) = (x2 – 1) |x2 – 3x +2| + cos ( | | ) is not differentiable at

Solution

Correct option is

2

The function f (x) = (x2 – 1) |x2 – 3x +2| + cos (|x|)          …(i) 

Here, | x | is not differentiable at x = 0 but

          

∴  cos (|x|) is differentiable at x = 0                               …(ii) 

  

         

        

Now, to check differentiability at x = 1, 2 (using shortcut method)

           

Thus, for f ' (1) we have 

             

Thus f (x) is differentiable at x = 1 

   

Thus, f (x) is not differentiable at x = 2

SIMILAR QUESTIONS

Q1

 for what value of kf (x) is continuous at x = 0?

Q2

      

Determine a and b such that f (x) is continuous at x = 0.

Q3

Find the points of discontinuity of 

Q4

 

   

Determine the form of g(x) = f ( f (x)) and hence find the point of discontinuity if g, if any.

Q5

The left hand derivative of f (x) = [x] sin (πx) at x = kk is an integer, is:

Q6

Which of the following functions is differentiable at x = 0?

Q7

Let f (x) = [n + p sin x], x Ïµ (0, π), n Ïµ Z and p is a prime number, where [.] denotes the greatest integer function. Then find the number of points where f (x) is not Differential.

Q8

, then draw the graph of f (x) in the interval [–2, 2] and discuss the continuity and differentiability in [–2, 2]

Q9

Fill in the blank, statement given below let . The set of points where f (x) is twice differentiable is ……………. .

Q10