Examine the differentiability of f(x) `=2x+|x-1|` at x = 1

Examine the differentiability of f(x) = 2x^(2)+ 1 at x = 1 .

A function f (x) is defined as follows : f(x)={{:(2-x",","when "xlt1),(x^(2)-3x",","when "xge1):} Examine the differentiability of the function f (x) at x= 1 , hence state whether f (x) is continuous at x = 1 or not .

Examine the differentiability of the function f(x)=|cosx| at x=(pi)/(2) .

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

Examine the differentiability of the function f(x) = {:{(x[x], if 0 lex<2),((x-1)x,if2lex<3):} at x =2

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

Let f: R rarr R (R is the set of real numbers) be defined as follows: f(x) = { : (2-x , if 1lexle2),(x-1/2x^2 ,if x ge 2) : Examine the continity and differentiability of f(x) at x=2.

Examine the continuity and differentiability of the function f(x)=3x+|x-1|"at "x=1