Question

The set of all points where the function  is differentiable is 

Solution

Correct option is

(–∞, ∞~ {0}

For x ≠ 0, we have

    

                        

  

because, as h → 0–, h is a negative number, so that

  

Here f is not differentiable at x = 0. Thus the points of differentiability are (– ∞, ∞) ~ {0}. 

SIMILAR QUESTIONS

Q1

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

Q2

If (2) = 4 and f’(2) = 1, then 

                    

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

               

Q10

Let

         

The values of the coefficient a and b for which the function is continuous and has a derivative at x0, are