Examine the differentiablity of f at x = 1,2, if
`f(x)={(x,0ltxlt1),(2x-x^2,1lexle2),(x-x^2/2,xgt2):}`

Examine differentiability at x= 1 and x=0 f(x)={(-x, x 1, ):}

Examine the differentiablity at x = 0,1,2 of the function f defined by f(x)={(4-x,xle0),(5x+4,0ltxle1),(4x^2-3x,1ltxlt2),(3x+4,xge2):}

Examine continuity at the given point of the function f defined by f(x)={(-x,xlt0),(x,0lexle1,),(2-x,xgt1,):} at x=0,1

Examine the continuity of f(x) = |x|+|x-2| at x =0 and at x =2

Examine continuity at the given point of the function f defined by f(x)={(1-x,0 lexle1),(x-1,xgt1,):} at x=1

Examine continuity at the given point of the function f defined by f(x)={(x,xlt1),(1,x=1,),(2-x,xgt1,at x =1):}

Discuss the continuity of the function f given by f(x) = {(2-x,x<2),(2+x,xge2):}

Sketch the graph of the function f given by f(x)={(-1,xle0),(x^2,x>0):}

Examine the continuity of the following function at the given point : f(x) = {(x, 0 le x < 1/2),(1, x = 1/2),(1-x, 1/2 < x < 1):} at x = 1/2 .

Examine continuity at the given point of the function f defined by f(x)={(-2,xlt0),(0,x=0,),(2,xgt0,at x =0):}