Is the function f (x) = |x2 - x| differentiable at x = 2. If yes find it’s derivative.

Question

Parvez ali · Answer

Thanks & Regards Parvez Ali askIITians Faculty

ruchi yadav · Answer

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
Askiitians Faculty

Sher Mohammad · Answer

yes, for x>1, f(x)=x^2-x f'(x)=2x-1 f'(2)=3 Sher Mohammad B.Tech, IIT Delhi.

Sher Mohammad · Answer

|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 Sher Mohammad B.Tech, IIT Delhi

Ajay Verma · Answer

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,

askIITians faculty,

IIT HYDERABAD

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Is the function f (x) = |x2 - x| differentiable at x = 2. If yes find it’s derivative.

Is the function f (x) = |x2 - x| differentiable at x = 2. If yes find it’s derivative.

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