Question

Find the set of points where x2 |x| is true thrice differentiable.

Solution

Correct option is

R – {0}

Let f (x) = x2 | | which could be expressed as, 

                        

  

So, f’ (x) exists for all real x.  

             

So, f’’(x) exists for all real x.  

          

However, f’’’(0) does not exists since f’’’ (0 –) = – 6 and f’’’(0+) = 6 which are not equal. Thus, the set of points where f (x) is thrice differentiable is R – {0}

SIMILAR QUESTIONS

Q1

Let f (x) = Ï•(x) + ψ(x) and Ï•(a), ψ’(a) are finite and definite. Then:

Q2

If f (x) = x + tan and g(x) is the inverse of f (x) then g’ (x) is equal to:

Q3

If f (x) is differentiable function and (f (x). g(x)) is differentiable at x = a, then

Q4

        

Determine the value of ‘a’ if possible, so that the function is continuous

Q5

 for all real x and y. If f ’ (0) exists and equals to –1and f (0) = 1, find f ’(x).

Q6

Now if it is given that there exists a positive real δ, such that f (h) = h for 0 < h < δ then find f’(x) and hence f (x).

Q7

Let f  be an even function and f ’(0) exists, then find f’(0).

Q8

Let f (x) = xnn being non-negative integer. Then find the value of n for which the equality f’(a + b) = f ’(a) + f ’ (b) is valid for all, ab > 0

Q9

 

Q10

Find the number of points where f (x) = [sin x + cos x(where [.] denotes greatest integral function), x Ïµ [0, 2π] is not continuous.