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Is the function f (x) = |x2 - x| differentiable at x = 2. If yes find it’s derivative. 7 years ago Thanks & Regards
Parvez Ali

7 years ago
Yes fuction will be differentiable at x =2. which can easily be seen by graph of the function.

First draw the graph of y = x2-x and then take mode.

Derivative will be = 2x-1
at x= 2
Derivative will be 4-1 = 3

Thank You
Ruchi Sher Mohammad IIT Delhi
7 years ago
|x(x-1)|=x(x-1) if x(x-1)>0 x belongs to (-inf,0) or (1,inf )
|x(x-1)|=x(x-1) x belongs to (0,1 )

for x>1
f'(x)=2x-1
f'(2)=3

B.Tech, IIT Delhi

7 years ago
f(x)= | x^2 - x |
at x=2 ( x^2 - x ) > 0

so we can take f(x) = x^2 - x

for differentiability
L.H.D = R.H.D

L.H. D = {f(a-h) - f(a)} / -h
= {f (2-h) - f(2)} / -h
= {(2-h)^2 - (2-h) - 2 } / -h
= 3

R.H.D = { f(2+h) - f(2)}/ h
= {(2+h)^2 - (2+h) - 2 } / h
= 3

so its differentiable
and derivative = 3

Thanks and Regards,
Ajay verma,