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Question: If f(x) =\(\sqrt{x}\). Then...

If f(x) =x\sqrt{x}. Then

A

f′(0+) and f′(0– ) do not exist

B

f′(0+) exists but f′(0– ) does not exist

C

f′(0+) = f′(0–)

D

None of these

Answer

f′(0+) and f′(0– ) do not exist

Explanation

Solution

As for the derivative f’(0) we have,

f′(0+) = lim⁡h→0hsin⁡1h−0h=lim⁡h→0sin⁡1h\lim _ { h \rightarrow 0 } \frac { h \sin \frac { 1 } { h } - 0 } { h } = \lim _ { h \rightarrow 0 } \sin \frac { 1 } { h } which doesn’t exist

Similarly, the limit f′(0–) doesn’t exist