﻿ 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). : Kaysons Education

# 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).

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## Question

### Solution

Correct option is

f’(x) = 1, f (x) = x

Given       f (h) = h

⇒      f ’ (x) = 1, integrating both sides we get,

⇒       f (x) = x + c

Where   f (0) = 0   ⇒      c = 0

so,         f (x) = x

Thus     f’ (x) = 1   and    f (x) = x

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