Find the derivative of f(x ) = x|x| , if `-1le x le 1`

Draw the graph of the function f(x) = x - |x - x^(2)|, -1 le x le 1 and discuss the continuity or discontinuity of f in the interval -1 le x le 1

Draw the graph of the function f(x)= x- |x-x^(2)|, -1 le x le 1 and find the points of non-differentiability.

Draw the graph of the function: f(x) = |1-x| + |1+x|, -2 le x le 2

The range of the function f(x)=|x-1|+|x-2|, -1 le x le 3, is

f(x)=|x-r|; r-1 le x le r + 1 and =1 ; r + 1 < x < r + r Find the fundamental period of f(x), if at all f(x) is periodic.

Let f(x) be defined on [-2,2] and is given by f(x) = {{:(x+1, - 2le x le 0 ),(x - 1, 0 le x le 2):} , then f (|x|) is defined as

If function f(x) = x-|x-x^(2)|, -1 le x le 1 then f is

Let f (x)= [{:(x ^(2)+a,0 le x lt 1),( 2x+b,1le x le 2):}and g (x)=[{:(3x+b,0 le x lt 1),(x ^(3), 1 le x le 2):} If derivative of f(x) w.r.t. g (x ) at x =1 exists and is equal to lamda, then which of the followig is/are correct?