Examine differentiability at x= 1 and x=0
`f(x)={(-x, x<0 "",),(x^2,0lexle1, ),(3, ""x^3-x+1x>1, ):}`

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

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):}

if f(x)={(x^2,xle1),(ax+b,x>1):} is differentiable at x = 1, find the values of a and b. Hence find f'(1)

Examine continuity of the function f defined by. f(x)=x-5

Find f0g and g0f : f(x)=x+1 , g(x)=cosx

f(x)={(x^2+2x, "" xle0,),(ax+b, "" x >0,):} is continuous and differentiable at x =0, find the values of a and b

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

Examine continuity of the function f defined by. f(x) =frac(1)(x-5)

find the points of discontinuity of the function f defined by f(x) = {(4x+1,x 0):}

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