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

# Find The Set Of Points Where x2 |x| Is True Thrice Differentiable.

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## Question

### 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}

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