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Is the function f (x) = |x2 - x| differentiable at x = 2. If yes find it’s derivative.
Thanks & RegardsParvez AliaskIITians Faculty
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-1at x= 2Derivative will be 4-1 = 3Thank YouRuchiAskiitians Faculty
yes,for x>1, f(x)=x^2-xf'(x)=2x-1f'(2)=3Sher MohammadB.Tech, IIT Delhi.
|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>1f'(x)=2x-1f'(2)=3Sher MohammadB.Tech, IIT Delhi
f(x)= | x^2 - x |at x=2 ( x^2 - x ) > 0so we can take f(x) = x^2 - xfor differentiabilityL.H.D = R.H.DL.H. D = {f(a-h) - f(a)} / -h= {f (2-h) - f(2)} / -h= {(2-h)^2 - (2-h) - 2 } / -h= 3R.H.D = { f(2+h) - f(2)}/ h= {(2+h)^2 - (2+h) - 2 } / h= 3so its differentiableand derivative = 3Thanks and Regards,Ajay verma,askIITians faculty,IIT HYDERABAD
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