The Set Of All Points Where The Function f (x) = x |x| Is Differentiable Is 

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Question

The set of all points where the function (x) = x |x| is differentiable is 

Solution

Correct option is

(0, )

Since x2 and –x2 are differentiable functions, f (x) is differentiable, except possibly at x = 0. 

                          [∵ f (0) = 0]                                                                                 

                        

                      

                      

Hence f is differentiable everywhere.  

Testing

SIMILAR QUESTIONS

Q1

If (2) = 4 and f’(2) = 1, then 

                    

Q2

The set of all points where the function  is differentiable is 

Q3

For n Ïµ N, let  The left hand derivative of f at x = π/4 is  

Q4

If f(a) = 2, f’(a) = 1, g(a) = –1 and g’(a) = 2, the value of

                       

Q5

If  is differentiable at x = 0, then

Q6

 

If f’ is differentiable function and f’’(x) is continuous at x = 0 and f’’(0) =a, the value of  

                  

Q7

Let [.] denote the greatest integer function and . Then

Q8

Let f (x + y) = (xf (y) for all x and y. If f (5) = 2 and f’(0) = 3, then f’(5) is equal to

Q9

 

Let f (x) = [x] and