examine the differentiability of `f(x)={[x^(2)+1, if 0<=x<=1],[3-x, if 1<=x<=2]` at `x=1`

Discuss the differentiability of f(x)={xsin(1nx^2),x!=0 0,x=0a tx=0

Examine the differentiability of f , where f is defined by f(x) = {{:(x[x],if0lexlt2),((x-1)x,if2lexlt3):} at x = 2

Examine the differentiability of f, where f is defined by f(x) = {{:(x[x],if0lexlt2),((x-1)x,if2lexlt3):} at x = 2

Examine the continuity and differentiability of f(x)=|x|+|x-1|+|x-2|x in R. Also drawthe graph of f(x)

Examine the differentiability of following function x=0,f(x)={e^(-(1)/(x^(2)))*sin((1)/(x))x!=0 and 0,x=0

Examine the differentiability of the function 'f' defined by : f(x)={{:(2x+3",if "-3lexlt-2),(x+1",if "-2lexlt0),(x+2",if "0lexle1):} .

Examine the differentiability of the function f defined by -2<=x<0x+2,quad if 0<=x<=f(x)={2x+3,quad if quad -3<=x<=-2x+1,quad if quad -2<=x<0x+2,quad if 0<=x<=

Examine the continuity of f(x) = {((sin2x)/(2x), x ne 0),(2, x = 0):} at x = 0