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

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

yes,

|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