If f x = x , where x is the greatest integer not greater than x, then f ' 1 + = ….

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Question: Answered & Verified by Expert

If

f (x) = [x]

, where

[x]

is the greatest integer not greater than x, then

f^{'} (1^{+})

= ….

MathematicsFunctionsMHT CETMHT CET 2019 (Shift 2)

Options:

A 1
B 2
C 0
D -1

Solution:

2525 Upvotes Verified Answer

The correct answer is: 0

We have,

f (x) = [x]

∴ f^{'} (1^{+}) = \underset{x \to 1^{+}}{l i m} \frac{f (x) - f (1)}{x - 1} = \underset{h \to 0}{l i m} \frac{f (1 + h) - f (1)}{h}

\underset{h \to 0}{l i m} \frac{[1 + h] - [1]}{h} \Rightarrow \underset{h \to 0}{l i m} \frac{1 - 1}{h} = 0

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