Question

If  is differentiable at x = 0, then

Solution

Correct option is

p + q = 0; r is any real number

It can be seen f’(0–) = –p –q and f’(0+) = p + q. Therefore, for f to be differentiable at x = 0, we must have p + q = 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

The set of all points where the function  is differentiable is 

Q4

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

Q5

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

                       

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