Consider a function s.t . Choose the correct option:

- is always diffrentiable.
- there exist atleast one such continuous but non-differentiable at exactly points and
- there exist atleast one such $f$ continuous s.t
- It is not possible to find a sequence of reals diverging to infinity s.t .

TIFR 2019 GS Part A, Problem 14

Analysis

Moderate

Real analysis Bartle and Sherbert

Do you really need a hint? Try it first!

for sure option 1) is not true any will give us the counter.

Observe that with have so that

whenever . What does it say about 3) and 4)?

whenever . What does it say about 3) and 4)?

This rules out (3) and (4) right away.

So (2) is the only option left.

So (2) is the only option left.

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